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Volumn , Issue , 2007, Pages 1-778

Linear partial differential equations for scientists and engineers

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EID: 84892345249     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-0-8176-4560-1     Document Type: Book
Times cited : (211)

References (186)
  • 5
    • 0001865962 scopus 로고
    • Model equations for long waves in nonlinear dispersive systems
    • Benjamin, T.B., Bona, J.L., and Mahony, J.J., Model equations for long waves in nonlinear dispersive systems, Phil. Trans. Roy. Soc. A272 (1972) 47-78.
    • (1972) Phil. Trans. Roy. Soc. , vol.A272 , pp. 47-78
    • Benjamin, T.B.1    Bona, J.L.2    Mahony, J.J.3
  • 11
    • 77956834067 scopus 로고
    • A mathematical model illustrating the theory of turbulence
    • Burgers, J.M., A mathematical model illustrating the theory of turbulence, Adv. Appl. Mech. 1 (1948) 171-191.
    • (1948) Adv. Appl. Mech. , vol.1 , pp. 171-191
    • Burgers, J.M.1
  • 12
    • 0005842809 scopus 로고
    • Dover Publications, New York
    • Byerly, W.E., Fourier Series, Dover Publications, New York (1959).
    • (1959) Fourier Series
    • Byerly, W.E.1
  • 13
    • 0001498106 scopus 로고
    • On the convergence and growth of partial sums of Fourier Series
    • Carleson, L., On the convergence and growth of partial sums of Fourier Series, Acta Mathematica, 116 (1966) 135-157.
    • (1966) Acta Mathematica , vol.116 , pp. 135-157
    • Carleson, L.1
  • 19
    • 0018524277 scopus 로고
    • The finite element method after twenty five years; A personal view
    • Clough, R.W., The finite element method after twenty five years; A personal view, Computer Structures 12 (1980) 361-370.
    • (1980) Computer Structures , vol.12 , pp. 361-370
    • Clough, R.W.1
  • 22
    • 0003620605 scopus 로고
    • Cambridge University Press, Cambridge
    • Copson, E.T., Asymptotic Expansions, Cambridge University Press, Cambridge (1965).
    • (1965) Asymptotic Expansions
    • Copson, E.T.1
  • 24
    • 84960798507 scopus 로고
    • Variational methods for the solutions of problems of equilibrium and vibrations
    • Courant, R., Variational methods for the solutions of problems of equilibrium and vibrations, Bull. Amer. Math. Soc. 49 (1943) 10-30.
    • (1943) Bull. Amer. Math. Soc. , vol.49 , pp. 10-30
    • Courant, R.1
  • 26
    • 0003908527 scopus 로고
    • Über die partiellen differenzengleichungen de mathematischen Physik
    • Courant, R., Friedrichs, K., and Lewy, H., Über die partiellen differenzengleichungen de mathematischen Physik, Mathematische Annalen 100 (1928) 32-74.
    • (1928) Mathematische Annalen , vol.100 , pp. 32-74
    • Courant, R.1    Friedrichs, K.2    Lewy, H.3
  • 27
    • 0004020231 scopus 로고
    • (Second Edition), Clarendon Press, Oxford
    • Crank, J., Mathematics of Diffusion (Second Edition), Clarendon Press, Oxford (1975).
    • (1975) Mathematics of Diffusion
    • Crank, J.1
  • 28
    • 84953600891 scopus 로고
    • A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type
    • Crank, J. and Nicholson, P., A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type, Proc. Camb. Phil. Soc. 43 (1947) 50-67.
    • (1947) Proc. Camb. Phil. Soc. , vol.43 , pp. 50-67
    • Crank, J.1    Nicholson, P.2
  • 30
    • 0014552591 scopus 로고
    • On asymptotic treatment of the transient development of surface waves
    • Debnath, L., On asymptotic treatment of the transient development of surface waves, Appl. Sci. Res. 21 (1969) 24-36.
    • (1969) Appl. Sci. Res. , vol.21 , pp. 24-36
    • Debnath, L.1
  • 31
    • 84892359124 scopus 로고
    • Unsteady axisymmetric capillary-gravity waves in a viscous liquid
    • Debnath, L., Unsteady axisymmetric capillary-gravity waves in a viscous liquid, Indian J. Pure and Appl. Math. 14 (1983) 540-553.
    • (1983) Indian J. Pure and Appl. Math. , vol.14 , pp. 540-553
    • Debnath, L.1
  • 32
    • 0004169230 scopus 로고
    • Cambridge University Press, Cambridge, England
    • Debnath, L., Nonlinear Waves, Cambridge University Press, Cambridge, England (1983).
    • (1983) Nonlinear Waves
    • Debnath, L.1
  • 33
    • 84892351678 scopus 로고
    • Solitons and the inverse scattering transforms
    • Debnath, L., Solitons and the inverse scattering transforms, Bull. Cal. Math. Soc. 84 (1992) 475-504.
    • (1992) Bull. Cal. Math. Soc. , vol.84 , pp. 475-504
    • Debnath, L.1
  • 36
    • 0034668466 scopus 로고    scopus 로고
    • Some nonlinear evolution equations in water waves
    • Debnath, L., Some nonlinear evolution equations in water waves, J. Math. Anal. Appl. 251 (2000) 488-503.
    • (2000) J. Math. Anal. Appl. , vol.251 , pp. 488-503
    • Debnath, L.1
  • 37
    • 84892332015 scopus 로고    scopus 로고
    • Nonlinear dynamics of water waves and breaking phenomena
    • Debnath, L., Nonlinear dynamics of water waves and breaking phenomena, Proc. Indian Nat. Sci. Acad. Special Volume (2002) 683-753.
    • (2002) Proc. Indian Nat. Sci. Acad. Special Volume , pp. 683-753
    • Debnath, L.1
  • 38
    • 17844394750 scopus 로고    scopus 로고
    • Fractional integral and fractional partial differential equation in fluid mechanics, Fractional Calculus Appl
    • Debnath, L., Fractional integral and fractional partial differential equation in fluid mechanics, Fractional Calculus Appl. Analysis 6 (2003) 119-155.
    • (2003) Analysis , vol.6 , pp. 119-155
    • Debnath, L.1
  • 39
    • 17844372193 scopus 로고    scopus 로고
    • Recent applications of fractional calculus to science and engineering
    • Debnath, L., Recent applications of fractional calculus to science and engineering, Internat. J. Math. & Math. Sci. 2003, No. 54 (2003) 3413-3442.
    • (2003) Internat. J. Math. & Math. Sci. 2003 , vol.54 , pp. 3413-3442
    • Debnath, L.1
  • 41
    • 33646887440 scopus 로고    scopus 로고
    • On solutions to few linear fractional inhomogeneous partial differential equations in fluid mechanics, Fractional Calculus Appl
    • Debnath, L. and Bhatta, D., On solutions to few linear fractional inhomogeneous partial differential equations in fluid mechanics, Fractional Calculus Appl. Analysis 7 (2004) 21-36.
    • (2004) Analysis , vol.7 , pp. 21-36
    • Debnath, L.1    Bhatta, D.2
  • 44
    • 44049116566 scopus 로고
    • The Cauchy-Poisson waves in an inviscid rotating stratified liquid
    • Debnath, L. and Rollins, D., The Cauchy-Poisson waves in an inviscid rotating stratified liquid, Internat. J. Nonlinear Mech. 27 (1992) 405-412.
    • (1992) Internat. J. Nonlinear Mech. , vol.27 , pp. 405-412
    • Debnath, L.1    Rollins, D.2
  • 45
    • 51249173839 scopus 로고
    • Three-dimensional nonlinear Schrodinger equation for finite-amplitude gravity waves in a fluid
    • 99B (1987) 247
    • Debnath, L. and Shivamoggi, B.K., Three-dimensional nonlinear Schrodinger equation for finite-amplitude gravity waves in a fluid, Nuovo Cimento 94B (1986) 140-148; 99B (1987) 247.
    • (1986) Nuovo Cimento , vol.94 B , pp. 140-148
    • Debnath, L.1    Shivamoggi, B.K.2
  • 46
    • 45149137658 scopus 로고
    • Pseudo-variational principles and nonlinear surface waves in a dissipative fluid
    • Debnath, L. and Shivamoggi, B.K., Pseudo-variational principles and nonlinear surface waves in a dissipative fluid, Internat. J. Nonlinear Mech. 25 (1990) 61-65.
    • (1990) Internat. J. Nonlinear Mech. , vol.25 , pp. 61-65
    • Debnath, L.1    Shivamoggi, B.K.2
  • 57
    • 0004278787 scopus 로고
    • (Translated By A. Freeman), Dover Publications, New York
    • Fourier, J.B.J., The Analytical Theory of Heat (Translated by A. Freeman), Dover Publications, New York (1955).
    • (1955) The Analytical Theory of Heat
    • Fourier, J.B.J.1
  • 60
    • 0003814292 scopus 로고
    • (Translated by R.A. Silverman), Prentice-Hall, Englewood Cliffs, New Jersey
    • Gelfand, I.M. and Fomin, S.V., Calculus of Variations (Translated by R.A. Silverman), Prentice-Hall, Englewood Cliffs, New Jersey (1963).
    • (1963) Calculus of Variations
    • Gelfand, I.M.1    Fomin, S.V.2
  • 61
    • 84892333173 scopus 로고    scopus 로고
    • Some exact solutions of nonlinear shallow water equations, Internal
    • Ghosh, K.K. and Debnath, L., Some exact solutions of nonlinear shallow water equations, Internal. J. Nonlinear Mech. 31 (1997) 104-108.
    • (1997) J. Nonlinear Mech. , vol.31 , pp. 104-108
    • Ghosh, K.K.1    Debnath, L.2
  • 63
    • 1542514243 scopus 로고
    • A new method of solution of certain boundary problems for equations of mathematical physics permitting of a separation of variables
    • Grunberg, G., A new method of solution of certain boundary problems for equations of mathematical physics permitting of a separation of variables, J. Phys. 10 (1946) 301-320.
    • (1946) J. Phys. , vol.10 , pp. 301-320
    • Grunberg, G.1
  • 72
    • 0002248582 scopus 로고
    • Integral equation method in potential theory. i
    • Jaswon, M.A., Integral equation method in potential theory. I, Proc. R. Soc. London, A 275 (1963) 23-32.
    • (1963) Proc. R. Soc. London, A , vol.275 , pp. 23-32
    • Jaswon, M.A.1
  • 79
  • 80
    • 0642304541 scopus 로고
    • The KdV equation and related problems in water wave theory
    • (ed. L. Debnath), Cambridge University Press, Cambridge
    • Johnson, R.S., The KdV equation and related problems in water wave theory, in Nonlinear Waves (ed. L. Debnath), 25-43, Cambridge University Press, Cambridge (1983).
    • (1983) Nonlinear Waves , pp. 25-43
    • Johnson, R.S.1
  • 87
    • 0001524186 scopus 로고
    • On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves
    • Korteweg, D.J. and de Vries, G., On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves, Phil. Mag. 39 (1895) 422-443.
    • (1895) Phil. Mag. , vol.39 , pp. 422-443
    • Korteweg, D.J.1    De Vries, G.2
  • 91
    • 0004168443 scopus 로고
    • (Sixth Edition), Cambridge University Press, Cambridge, England
    • Lamb, H., Hydrodynamics (Sixth Edition), Cambridge University Press, Cambridge, England (1932).
    • (1932) Hydrodynamics
    • Lamb, H.1
  • 92
    • 84980078953 scopus 로고
    • Weak solutions of nonlinear hyperbolic equations and their numerical computation
    • Lax, P.D.,Weak solutions of nonlinear hyperbolic equations and their numerical computation, Comm. Pure Appl. Math. 7 (1954) 159-193.
    • (1954) Comm. Pure Appl. Math. , vol.7 , pp. 159-193
    • Lax, P.D.1
  • 93
    • 0009045631 scopus 로고
    • The initial-value problem for nonlinear hyperbolic equations in two independent variables
    • (Princeton)
    • Lax, P.D., The initial-value problem for nonlinear hyperbolic equations in two independent variables, Ann. Math. Stud. (Princeton) 33 (1954) 211-299.
    • (1954) Ann. Math. Stud. , vol.33 , pp. 211-299
    • Lax, P.D.1
  • 94
    • 84980077727 scopus 로고
    • Hyperbolic systems of conservation law, II
    • Lax, P.D., Hyperbolic systems of conservation law, II, Comm. Pure Appl. Math. 10 (1957) 537-566.
    • (1957) Comm. Pure Appl. Math. , vol.10 , pp. 537-566
    • Lax, P.D.1
  • 96
    • 33750483511 scopus 로고
    • Development of singularities of solutions of nonlinear hyperbolic partial differential equations
    • Lax, P.D., Development of singularities of solutions of nonlinear hyperbolic partial differential equations, J. Math. Phys. 5 (1964) 611-613.
    • (1964) J. Math. Phys. , vol.5 , pp. 611-613
    • Lax, P.D.1
  • 97
    • 84981754671 scopus 로고
    • Integrals of nonlinear equations of evolution and solitary waves
    • Lax, P.D., Integrals of nonlinear equations of evolution and solitary waves, Comm. Pure Appl. Math. 21 (1968) 467-490.
    • (1968) Comm. Pure Appl. Math. , vol.21 , pp. 467-490
    • Lax, P.D.1
  • 98
    • 0001299964 scopus 로고
    • The formation and decay of shock waves
    • Lax, P.D., The formation and decay of shock waves, Amer. Math. Monthly 79 (1972) 227-241.
    • (1972) Amer. Math. Monthly , vol.79 , pp. 227-241
    • Lax, P.D.1
  • 100
    • 84980148156 scopus 로고
    • Periodic solutions of the Korteweg-de Vries equation
    • Lax, P.D., Periodic solutions of the Korteweg-de Vries equation, Comm. Pure Appl. Math. 28 (1975) 141-188.
    • (1975) Comm. Pure Appl. Math. , vol.28 , pp. 141-188
    • Lax, P.D.1
  • 101
    • 0002094831 scopus 로고
    • A Hamiltonian approach to the KdV and other equations
    • (ed. M. Crandall), Academic Press, New York
    • Lax, P.D., A Hamiltonian approach to the KdV and other equations, in Nonlinear Evolution Equations (ed. M. Crandall), Academic Press, New York (1978) 207-224.
    • (1978) Nonlinear Evolution Equations , pp. 207-224
    • Lax, P.D.1
  • 103
  • 105
    • 0004289888 scopus 로고
    • Cambridge University Press, Cambridge
    • Lighthill, M.J., Waves in Fluids, Cambridge University Press, Cambridge (1980).
    • (1980) Waves in Fluids
    • Lighthill, M.J.1
  • 106
    • 0003591813 scopus 로고    scopus 로고
    • (Second Edition) John Wiley, New York
    • Logan, J.D., Applied Mathematics (Second Edition), John Wiley, New York (1997).
    • (1997) Applied Mathematics
    • Logan, J.D.1
  • 107
    • 0001869174 scopus 로고
    • On the initial-value problem for the fractional diffusion-wave equation
    • (ed. S. Rionero and T. Ruggeri), World Scientific, Singapore)
    • Mainardi, F., On the initial-value problem for the fractional diffusion-wave equation, in Waves and Stability in Continuous Media (ed. S. Rionero and T. Ruggeri), World Scientific, Singapore (1994) 246-251.
    • (1994) Waves and Stability in Continuous Media , pp. 246-251
    • Mainardi, F.1
  • 108
    • 0029427754 scopus 로고
    • The time fractional diffusion-wave equation
    • Mainardi, F., The time fractional diffusion-wave equation, Radiofisika 38 (1995) 20-36.
    • (1995) Radiofisika , vol.38 , pp. 20-36
    • Mainardi, F.1
  • 109
    • 0030464353 scopus 로고    scopus 로고
    • Fractional relaxation-oscillation and fractional diffusion-wave phenomena
    • Mainardi, F., Fractional relaxation-oscillation and fractional diffusion-wave phenomena, Chaos, Solitons, Fractals 7 (1996) 1461-1477.
    • (1996) Chaos, Solitons, Fractals , vol.7 , pp. 1461-1477
    • Mainardi, F.1
  • 118
    • 0022492943 scopus 로고
    • The realization of the generalized transfer equation in a medium with fractal geometry
    • (b)
    • Nigmatullin, R.R., The realization of the generalized transfer equation in a medium with fractal geometry, Phys. Sta. Sol. (b) 133 (1986) 425-430.
    • (1986) Phys. Sta. Sol. , vol.133 , pp. 425-430
    • Nigmatullin, R.R.1
  • 123
    • 0343197439 scopus 로고
    • Generation of the hierarchies of solitons and generalized structure of the commutator representation, Acta
    • Qiao, Z., Generation of the hierarchies of solitons and generalized structure of the commutator representation, Acta. Appl. Math. Sinica 18 (1995) 287-301.
    • (1995) Appl. Math. Sinica , vol.18 , pp. 287-301
    • Qiao, Z.1
  • 124
    • 0037107993 scopus 로고    scopus 로고
    • Negative order MKdV hierarchy and a new integrable Neumann-like system
    • Qiao, Z. and Strampp, W., Negative order MKdV hierarchy and a new integrable Neumann-like system, Physica A 313 (2002) 365-380.
    • (2002) Physica A , vol.313 , pp. 365-380
    • Qiao, Z.1    Strampp, W.2
  • 126
    • 0003951930 scopus 로고
    • Dover Publications, New York
    • Rayleigh, Lord, The Theory of Sound, Vol. I (1894), Vol. 2 (1896), Dover Publications, New York.
    • (1894) The Theory of Sound , vol.1-2
    • Rayleigh, L.1
  • 129
    • 0004258932 scopus 로고
    • (Second Edition), Cambridge University Press, Cambridge
    • Roach, G.F., Green's Functions (Second Edition), Cambridge University Press, Cambridge (1982).
    • (1982) Green's Functions
    • Roach, G.F.1
  • 133
    • 0001553919 scopus 로고
    • Fractional diffusion and wave equations
    • Schneider, W.R. and Wyss, W., Fractional diffusion and wave equations, J. Math. Phys. 30 (1989) 134-144.
    • (1989) J. Math. Phys. , vol.30 , pp. 134-144
    • Schneider, W.R.1    Wyss, W.2
  • 145
    • 44949290847 scopus 로고
    • Asymptotic stability of solutions of the generalized Burgers equation
    • Soewono, E. and Debnath, L., Asymptotic stability of solutions of the generalized Burgers equation, J. Math. Anal. Appl. 153 (1990) 179-189.
    • (1990) J. Math. Anal. Appl. , vol.153 , pp. 179-189
    • Soewono, E.1    Debnath, L.2
  • 146
    • 0005245462 scopus 로고
    • Classification of self-similar solutions to a generalized Burgers equation
    • Soewono, E. and Debnath, L., Classification of self-similar solutions to a generalized Burgers equation, J. Math. Anal. Appl. 184 (1994) 389-398.
    • (1994) J. Math. Anal. Appl. , vol.184 , pp. 389-398
    • Soewono, E.1    Debnath, L.2
  • 151
    • 0003933895 scopus 로고
    • Interscience New York
    • Stoker, J.J., Water Waves, Interscience, New York (1957).
    • (1957) Water Waves
    • Stoker, J.J.1
  • 152
    • 0000025473 scopus 로고
    • On the theory of oscillatory waves
    • Stoker, G., On the theory of oscillatory waves, Trans. Camb. Phil. Soc. 8 (1847) 197-229.
    • (1847) Trans. Camb. Phil. Soc. , vol.8 , pp. 197-229
    • Stoker, G.1
  • 154
    • 0038676237 scopus 로고
    • Integral equation method in potential theory
    • Symm, G.T., Integral equation method in potential theory, Proc. Roy Soc. London A275 (1963) 33-46.
    • (1963) Proc. Roy Soc. London , vol.A275 , pp. 33-46
    • Symm, G.T.1
  • 158
    • 27644471908 scopus 로고
    • Vibration of a chain with nonlinear interaction
    • Toda, M., Vibration of a chain with nonlinear interaction, J. Phys. Soc. Japan 22 (1967) 431-436.
    • (1967) J. Phys. Soc. Japan , vol.22 , pp. 431-436
    • Toda, M.1
  • 159
    • 0003963664 scopus 로고
    • Prentice-Hall, Englewood Cliffs, New Jersey
    • Tolstov, G.P., Fourier Series, Prentice-Hall, Englewood Cliffs, New Jersey (1962).
    • (1962) Fourier Series
    • Tolstov, G.P.1
  • 165
    • 0042033287 scopus 로고
    • A general approach to linear and nonlinear dispersive waves using a Lagrangian
    • Whitham, G.B., A general approach to linear and nonlinear dispersive waves using a Lagrangian, J. Fluid Mech. 22 (1965) 273-283.
    • (1965) J. Fluid Mech. , vol.22 , pp. 273-283
    • Whitham, G.B.1
  • 166
    • 0001693596 scopus 로고
    • A new approach to problems of shock dynamics. Part I. Two dimensional problems
    • Whitham, G.B., A new approach to problems of shock dynamics. Part I. Two dimensional problems, J. Fluid Mech. 2 (1975) 146-171.
    • (1975) J. Fluid Mech. , vol.2 , pp. 146-171
    • Whitham, G.B.1
  • 170
    • 33846361348 scopus 로고
    • Interaction of Solitons in a Collisionless Plasma and Recurrence of Initial States
    • Zabusky, N.J. and Kruskal, M.D., Interaction of Solitons in a Collisionless Plasma and Recurrence of Initial States, Phys. Rev. Lett. 15 (1965) 240-243.
    • (1965) Phys. Rev. Lett. , vol.15 , pp. 240-243
    • Zabusky, N.J.1    Kruskal, M.D.2
  • 171
    • 0002557939 scopus 로고
    • Exact theory of two-dimensional self-focusing and one-dimensional self modulation of waves in nonlinear media
    • Zakharov, V.E. and Shabat, A.B., Exact Theory of Two-Dimensional Self-Focusing and One-Dimensional Self Modulation of Waves in Nonlinear Media, Sov. Phys. JETP 34 (1972) 62-69.
    • (1972) Sov. Phys. JETP , vol.34 , pp. 62-69
    • Zakharov, V.E.1    Shabat, A.B.2
  • 172
    • 0000169358 scopus 로고
    • Interaction between solitons in a stable medium
    • Zakharov, V.E. and Shabat, A.B., Interaction Between Solitons in a Stable Medium, Sov. Phys. JETP 37 (1974) 823-828.
    • (1974) Sov. Phys. JETP , vol.37 , pp. 823-828
    • Zakharov, V.E.1    Shabat, A.B.2
  • 174
    • 0002726347 scopus 로고
    • Finite elements in the solutions of field problems
    • Zienkiewicz, O.C. and Cheung, Y.K., Finite elements in the solutions of field problems, Engineer. 220 (1965) 370-507.
    • (1965) Engineer , vol.220 , pp. 370-507
    • Zienkiewicz, O.C.1    Cheung, Y.K.2
  • 186
    • 84892258400 scopus 로고
    • Problems on the equations of mathematical physics
    • Smirnov, M.M., Problems on the Equations of Mathematical Physics, Noordhoff (1967).
    • (1967) Noordhoff
    • Smirnov, M.M.1


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