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Volumn 3, Issue 4, 2004, Pages 883-919

Exponential Besov spaces and their applications to certain evolution equations with dissipation

Author keywords

Cauchy Riemann equation; Exponential Besov space; Initial value problem; Regularity of solutions; Rough initial data; Semi linear parabolic equation; Semi linear viscoelastic equation

Indexed keywords


EID: 24944440326     PISSN: 15340392     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (10)

References (41)
  • 1
    • 0008894832 scopus 로고
    • Kinetic relations and the propagation of phase boundaries in solids
    • R. Abeyaratne and J. K. Knowles, Kinetic relations and the propagation of phase boundaries in solids, Arch. Rational Mech. Analysis, 114 (1991), 119-154.
    • (1991) Arch. Rational Mech. Analysis , vol.114 , pp. 119-154
    • Abeyaratne, R.1    Knowles, J.K.2
  • 2
    • 0026237436 scopus 로고
    • Implitions of viscosity and stain gradient effects for the kinetics of propagation phase boundaries in solids
    • R. Abeyaratne and J. K. Knowles, Implitions of viscosity and stain gradient effects for the kinetics of propagation phase boundaries in solids, SIAM J. Appl. Math., 51 (1991), 1205-1221.
    • (1991) SIAM J. Appl. Math. , vol.51 , pp. 1205-1221
    • Abeyaratne, R.1    Knowles, J.K.2
  • 3
    • 0000823596 scopus 로고    scopus 로고
    • The initial value problem for the generalized Burgers equation
    • D. Bekiranov, The initial value problem for the generalized Burgers equation, Diff. and Integ. Eqns, 9 (1996), 1253-1265.
    • (1996) Diff. and Integ. Eqns , vol.9 , pp. 1253-1265
    • Bekiranov, D.1
  • 5
    • 0004434530 scopus 로고    scopus 로고
    • Multidimensional Kuramoto-Sivashinsky type equations
    • H. Biagioni and T. Gramchev, Multidimensional Kuramoto-Sivashinsky type equations, Math. Contemp., 115 (1998), 21-42.
    • (1998) Math. Contemp. , vol.115 , pp. 21-42
    • Biagioni, H.1    Gramchev, T.2
  • 6
    • 34250084341 scopus 로고
    • Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations I and II
    • J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations I and II, Geom. Funct. Anal., 3 (1993), 107-156; 209-262.
    • (1993) Geom. Funct. Anal. , vol.3 , pp. 107-156
    • Bourgain, J.1
  • 7
    • 0003230767 scopus 로고    scopus 로고
    • The global solutions of nonlinear Schrödinger equations
    • J. Bourgain, The global solutions of nonlinear Schrödinger equations, Amer. Math. Soc., 1999.
    • (1999) Amer. Math. Soc.
    • Bourgain, J.1
  • 8
    • 0002486767 scopus 로고
    • Global classical solutions of nonlinear wave equations
    • P. Brenner and W. von Wahl, Global classical solutions of nonlinear wave equations, Math. Z., 176 (1981), 87-121.
    • (1981) Math. Z. , vol.176 , pp. 87-121
    • Brenner, P.1    Von Wahl, W.2
  • 11
    • 23244434956 scopus 로고    scopus 로고
    • Polynomial upper bounds for the instability of the nonlinear Schrödinger equation below the energy norm
    • J. E. Colliander, M. Keel, G. Staffilani, H. Takaoka and T. Tao, Polynomial upper bounds for the instability of the nonlinear Schrödinger equation below the energy norm, Commun. on Pure and Applied Anal., 2 (2003), 33-50.
    • (2003) Commun. on Pure and Applied Anal. , vol.2 , pp. 33-50
    • Colliander, J.E.1    Keel, M.2    Staffilani, G.3    Takaoka, H.4    Tao, T.5
  • 12
    • 0037254091 scopus 로고    scopus 로고
    • Polynomial upper bounds for the orbital instability of the ID cubic NLS below the energy norm
    • J. E. Colliander, M. Keel, G. Staffilani, H. Takaoka and T. Tao, Polynomial upper bounds for the orbital instability of the ID cubic NLS below the energy norm, Discrete Contin. Dyn. Syst., 9 (2003), 31-50.
    • (2003) Discrete Contin. Dyn. Syst. , vol.9 , pp. 31-50
    • Colliander, J.E.1    Keel, M.2    Staffilani, G.3    Takaoka, H.4    Tao, T.5
  • 13
    • 0030537418 scopus 로고    scopus 로고
    • Non-uniqueness and uniqueness in the initial value problem for Burgers' equation
    • D. B. Dix, Non-uniqueness and uniqueness in the initial value problem for Burgers' equation, SIAM J.Math. Anal., 27 (1996), 708-724.
    • (1996) SIAM J.Math. Anal. , vol.27 , pp. 708-724
    • Dix, D.B.1
  • 14
    • 0000650977 scopus 로고
    • On some nonexistence and nonuniqueness theorems for nonlinear parabolic equations
    • H. Fujita, On some nonexistence and nonuniqueness theorems for nonlinear parabolic equations, Proc. Symp. Pure Math., 18 (1968), 131-136.
    • (1968) Proc. Symp. Pure Math. , vol.18 , pp. 131-136
    • Fujita, H.1
  • 15
    • 0039768823 scopus 로고    scopus 로고
    • The Cauchy problem in local spaces for the complex Ginzburg-Landau equation (II) Contraction Methods
    • J. Ginibre and G. Velo, The Cauchy problem in local spaces for the complex Ginzburg-Landau equation (II) Contraction Methods, Commun. Math. Phys., 187 (1997), 45-79.
    • (1997) Commun. Math. Phys. , vol.187 , pp. 45-79
    • Ginibre, J.1    Velo, G.2
  • 16
    • 46149140458 scopus 로고
    • p and regularity of weak solutions of the Navier-Stokes system
    • p and regularity of weak solutions of the Navier-Stokes system, Journal of Differential Equations, 61 (1986), 186-212.
    • (1986) Journal of Differential Equations , vol.61 , pp. 186-212
    • Giga, Y.1
  • 18
    • 0034354310 scopus 로고    scopus 로고
    • On convergence of solutions to the equation of viscoelasticity with capillarity
    • K. H. Hoffmann and P. Rybka, On convergence of solutions to the equation of viscoelasticity with capillarity, Comm. Part. Diff. Eqns., 25 (2000), 1845-1890.
    • (2000) Comm. Part. Diff. Eqns. , vol.25 , pp. 1845-1890
    • Hoffmann, K.H.1    Rybka, P.2
  • 20
    • 84963057299 scopus 로고
    • The Navier-Stokes equation with weak initial data
    • T. Kato and G. Ponce, The Navier-Stokes equation with weak initial data, Inter. Math. Research Note, 10 (1994), 435-444.
    • (1994) Inter. Math. Research Note , vol.10 , pp. 435-444
    • Kato, T.1    Ponce, G.2
  • 21
    • 0001138601 scopus 로고    scopus 로고
    • Endpoint Strichartz estimates
    • M. Keel and T. Tao, Endpoint Strichartz estimates, Amer. J. of Math., 120 (1998), 955-980.
    • (1998) Amer. J. of Math. , vol.120 , pp. 955-980
    • Keel, M.1    Tao, T.2
  • 22
    • 84974004169 scopus 로고
    • The Cauchy problem for the KdV equation in Sobolev spaces of negative indices
    • C. E. Kenig, G. Ponce and L. Vega, The Cauchy problem for the KdV equation in Sobolev spaces of negative indices, Duke Math. J., 71 (1993), 1-21.
    • (1993) Duke Math. J. , vol.71 , pp. 1-21
    • Kenig, C.E.1    Ponce, G.2    Vega, L.3
  • 23
    • 0030528276 scopus 로고    scopus 로고
    • A bilinear estimate with applications to the KdV equation
    • C. E. Kenig, G. Ponce and L. Vega, A bilinear estimate with applications to the KdV equation, J. Amer. Math. Soc., 9 (1996), 573-603.
    • (1996) J. Amer. Math. Soc. , vol.9 , pp. 573-603
    • Kenig, C.E.1    Ponce, G.2    Vega, L.3
  • 25
    • 0000873295 scopus 로고    scopus 로고
    • Distribution-valued initial data for the complex Ginzburg-Landau equation
    • C. D. Levermore and M. Oliver, Distribution-valued initial data for the complex Ginzburg-Landau equation, Commun. Partial Diff. Equations, 22 (1997), 39-48.
    • (1997) Commun. Partial Diff. Equations , vol.22 , pp. 39-48
    • Levermore, C.D.1    Oliver, M.2
  • 26
    • 0000781993 scopus 로고    scopus 로고
    • The complex Ginzburg-Landau equation as a model problem
    • C. D. Levermore and M. Oliver, The complex Ginzburg-Landau equation as a model problem, Lectures in Appl. Math., 31 (1996), 141-190.
    • (1996) Lectures in Appl. Math. , vol.31 , pp. 141-190
    • Levermore, C.D.1    Oliver, M.2
  • 27
    • 0005360710 scopus 로고    scopus 로고
    • The Cauchy problem for dissipative Korteweg de Vries equations in Sobolev spaces of Negative order
    • L. Molinet and F. Ribaud, The Cauchy problem for dissipative Korteweg de Vries equations in Sobolev spaces of Negative order, Indiana Univ. Math. J., 50 (2001), 1745-1776.
    • (2001) Indiana Univ. Math. J. , vol.50 , pp. 1745-1776
    • Molinet, L.1    Ribaud, F.2
  • 28
    • 0039807266 scopus 로고
    • Applications de la théorie des espaces d'interpolation dans l'analyse harmonique
    • J. Peetre, Applications de la théorie des espaces d'interpolation dans l'analyse harmonique, Ricerche Mat., (1966), 1-34.
    • (1966) Ricerche Mat. , pp. 1-34
    • Peetre, J.1
  • 31
    • 0001597155 scopus 로고
    • Regularity results for nonlinear wave equations
    • J. Shatah and M. Struwe, Regularity results for nonlinear wave equations, Ann. of Math., 138 (1993), 503-518.
    • (1993) Ann. of Math. , vol.138 , pp. 503-518
    • Shatah, J.1    Struwe, M.2
  • 32
    • 0020500507 scopus 로고
    • Admissibility criteria for propagating phase boundaries in a van der Waals fluid
    • M. Slemrod, Admissibility criteria for propagating phase boundaries in a van der Waals fluid, Arch. Rational Mech. Analysis, 81 (1983), 301-315.
    • (1983) Arch. Rational Mech. Analysis , vol.81 , pp. 301-315
    • Slemrod, M.1
  • 34
    • 24944487213 scopus 로고    scopus 로고
    • 2 functions, and applications to nonlinear dispersive equations
    • 2 functions, and applications to nonlinear dispersive equations, Amer. J. of Math., (2000).
    • (2000) Amer. J. of Math.
    • Tao, T.1
  • 36
    • 0001087444 scopus 로고
    • Equilibrium phase boundaries
    • L. Truskinovsky, Equilibrium phase boundaries, Dokl. Akad. Nauk SSSR, 275 (1982), 306-310.
    • (1982) Dokl. Akad. Nauk SSSR , vol.275 , pp. 306-310
    • Truskinovsky, L.1
  • 38
    • 0036116542 scopus 로고    scopus 로고
    • The limit behavoir of solutions for the complex Ginzburg-Landau equation
    • Baoxiang Wang, The limit behavoir of solutions for the complex Ginzburg-Landau equation, Communications on Pure Applied Mathematics, 55 (2002), 481-508.
    • (2002) Communications on Pure Applied Mathematics , vol.55 , pp. 481-508
    • Wang, B.1
  • 39
    • 51249183619 scopus 로고
    • Existence and nonexistencc of global solutions for a semilinear heat equation
    • F. B. Weissler, Existence and nonexistencc of global solutions for a semilinear heat equation, Israel Math. J., 39 (1981), 29-40.
    • (1981) Israel Math. J. , vol.39 , pp. 29-40
    • Weissler, F.B.1
  • 40
    • 0011432341 scopus 로고    scopus 로고
    • The complex Ginzburg-Landau equation with data in Sobolev spaces of negative indices
    • J. Wu, The complex Ginzburg-Landau equation with data in Sobolev spaces of negative indices, Houston J. Math., 25 (1999), 387-397.
    • (1999) Houston J. Math. , vol.25 , pp. 387-397
    • Wu, J.1
  • 41
    • 24944531331 scopus 로고    scopus 로고
    • On the Lyapanov functions for the solutions of the generalized Burgers equation
    • E. Zahrouni, On the Lyapanov functions for the solutions of the generalized Burgers equation, Commun, on Pure and Appl. Anal., 2 (2003), 383-402.
    • (2003) Commun, on Pure and Appl. Anal. , vol.2 , pp. 383-402
    • Zahrouni, E.1


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