메뉴 건너뛰기




Volumn 4, Issue 3, 2004, Pages 251-272

Emergence of waves in a nonlinear convection-reaction-diffusion equation

Author keywords

Asymptotic behaviour of solutions; Nonlinear diffusion; Travelling waves

Indexed keywords


EID: 4644348614     PISSN: 15361365     EISSN: None     Source Type: Journal    
DOI: 10.1515/ans-2004-0302     Document Type: Article
Times cited : (27)

References (30)
  • 1
    • 0008270784 scopus 로고
    • Density-dependent interaction-diffusion systems
    • Academic Press, New York
    • D. Aronson, Density-dependent interaction-diffusion systems, in Dynamics and Modeling of Reactive Systems, Academic Press, New York, 1980.
    • (1980) Dynamics and Modeling of Reactive Systems
    • Aronson, D.1
  • 2
    • 0000701823 scopus 로고
    • Positivity versus localization in degenerate diffusion equation
    • M. Bertsch, R. Kersner and L.A. Peletier, Positivity versus localization in degenerate diffusion equation, Nonlinear Anal. 9 (1985), 987-1008.
    • (1985) Nonlinear Anal. , vol.9 , pp. 987-1008
    • Bertsch, M.1    Kersner, R.2    Peletier, L.A.3
  • 3
    • 4644339074 scopus 로고    scopus 로고
    • Stability of travelling waves for degenerate reaction-diffusion equations of KPP-type
    • Z. Biro, Stability of travelling waves for degenerate reaction-diffusion equations of KPP-type, Adv. Nonlinear Studies 2 (2002), 357-371.
    • (2002) Adv. Nonlinear Studies , vol.2 , pp. 357-371
    • Biro, Z.1
  • 5
    • 0002449197 scopus 로고
    • Continuity of weak solutions to a general porous media equation
    • E. DiBenedetto, Continuity of weak solutions to a general porous media equation, Ind. Univ. Math. J. 32 (1983), 83-118.
    • (1983) Ind. Univ. Math. J. , vol.32 , pp. 83-118
    • Dibenedetto, E.1
  • 6
    • 0039346559 scopus 로고    scopus 로고
    • 1 stability of shock waves in scalar viscous conservation laws
    • 1 stability of shock waves in scalar viscous conservation laws, Commun. Pure Appl. Math. 51 (1998), 291-301.
    • (1998) Commun. Pure Appl. Math. , vol.51 , pp. 291-301
    • Freistühler, H.1    Serre, D.2
  • 7
    • 0242281412 scopus 로고    scopus 로고
    • (Birkhäuser Verlag, Basel) to appear. In electronic preprint form: Memorandum No. 1585, Faculty of Mathematical Sciences, University of Twente
    • B.H. Gilding and R. Kersner, Travelling waves in Nonlinear Reaction-Convection-Diffusion, (Birkhäuser Verlag, Basel, 2004) to appear. In electronic preprint form: Memorandum No. 1585, Faculty of Mathematical Sciences, University of Twente, 2001 (www.math.utwente.nl/publications).
    • (2001) Travelling Waves in Nonlinear Reaction-convection-diffusion
    • Gilding, B.H.1    Kersner, R.2
  • 9
    • 84862599035 scopus 로고
    • Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations
    • A.S. Kalashnikov, Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations, Russian Math. Surv. 42 (1987), 169-222.
    • (1987) Russian Math. Surv. , vol.42 , pp. 169-222
    • Kalashnikov, A.S.1
  • 10
    • 17044388042 scopus 로고    scopus 로고
    • Convergence to the travelling wave solution for a nonlinear reaction-diffusion equation
    • to appear
    • S. Kamin and P. Rosenau, Convergence to the Travelling Wave Solution for a Nonlinear Reaction-Diffusion Equation, Rendiconti Mat. Acc. Lincei (to appear).
    • Rendiconti Mat. Acc. Lincei
    • Kamin, S.1    Rosenau, P.2
  • 11
    • 0007223618 scopus 로고
    • The behaviour of solutions of the Cauchy problem when the time tends to infinity in the case of quasilinear equations arising in the theory of combustion
    • Ya.I. Kanel', The behaviour of solutions of the Cauchy problem when the time tends to infinity in the case of quasilinear equations arising in the theory of combustion, Soviet Math. Dokl. 1 (1960), 533-536. Translation of: Dokl. Akad. Nauk SSSR 132 (1960), 268-271.
    • (1960) Soviet Math. Dokl. , vol.1 , pp. 533-536
    • Kanel, Ya.I.1
  • 12
    • 0041661066 scopus 로고
    • Translation of
    • Ya.I. Kanel', The behaviour of solutions of the Cauchy problem when the time tends to infinity in the case of quasilinear equations arising in the theory of combustion, Soviet Math. Dokl. 1 (1960), 533-536. Translation of: Dokl. Akad. Nauk SSSR 132 (1960), 268-271.
    • (1960) Dokl. Akad. Nauk SSSR , vol.132 , pp. 268-271
  • 13
    • 0000632472 scopus 로고
    • Some properties of generalized solutions of quasilinear degenerate parabolic equations
    • R. Kersner, Some properties of generalized solutions of quasilinear degenerate parabolic equations, Acta Math. Acad. Sc. Hungaricae 32 (1978), 301-330.
    • (1978) Acta Math. Acad. Sc. Hungaricae , vol.32 , pp. 301-330
    • Kersner, R.1
  • 14
    • 0002722044 scopus 로고
    • Étude de l'équation de la diffusion avec croissance de la quantité de matierè et son application a un problème biologique
    • A. Kolmogorov, I. Petrovsky and N. Piscunov, Étude de l'équation de la diffusion avec croissance de la quantité de matierè et son application a un problème biologique, Bulletin Univ. Moscow, Ser. Internationale, Math., Mec. 1 (1937), 1-25. English translation in P. Pelcé, (ed.), Dynamics of Curved Fronts, Academic Press, Boston, 1988, 105-130; and O.A. Oleinik, (ed.), I.G. Petrowsky Selected Works Part II. Differential Equations and Probability Theory, Gordon and Breach, Amsterdam, 1996, 106-132.
    • (1937) Bulletin Univ. Moscow, Ser. Internationale, Math., Mec. , vol.1 , pp. 1-25
    • Kolmogorov, A.1    Petrovsky, I.2    Piscunov, N.3
  • 15
    • 0004243252 scopus 로고
    • English translation in, Academic Press, Boston
    • A. Kolmogorov, I. Petrovsky and N. Piscunov, Étude de l'équation de la diffusion avec croissance de la quantité de matierè et son application a un problème biologique, Bulletin Univ. Moscow, Ser. Internationale, Math., Mec. 1 (1937), 1-25. English translation in P. Pelcé, (ed.), Dynamics of Curved Fronts, Academic Press, Boston, 1988, 105-130; and O.A. Oleinik, (ed.), I.G. Petrowsky Selected Works Part II. Differential Equations and Probability Theory, Gordon and Breach, Amsterdam, 1996, 106-132.
    • (1988) Dynamics of Curved Fronts , pp. 105-130
    • Pelcé, P.1
  • 16
    • 0042587727 scopus 로고    scopus 로고
    • Gordon and Breach, Amsterdam
    • A. Kolmogorov, I. Petrovsky and N. Piscunov, Étude de l'équation de la diffusion avec croissance de la quantité de matierè et son application a un problème biologique, Bulletin Univ. Moscow, Ser. Internationale, Math., Mec. 1 (1937), 1-25. English translation in P. Pelcé, (ed.), Dynamics of Curved Fronts, Academic Press, Boston, 1988, 105-130; and O.A. Oleinik, (ed.), I.G. Petrowsky Selected Works Part II. Differential Equations and Probability Theory, Gordon and Breach, Amsterdam, 1996, 106-132.
    • (1996) I.G. Petrowsky Selected Works Part II. Differential Equations and Probability Theory , pp. 106-132
    • Oleinik, O.A.1
  • 17
    • 0345116415 scopus 로고    scopus 로고
    • Sharp profiles in degenerate and doubly degenerate Fisher-KPP equations
    • L. Malaguti and C. Marcelli, Sharp profiles in degenerate and doubly degenerate Fisher-KPP equations, J. Diff. Equations 195 (2003), 471-496.
    • (2003) J. Diff. Equations , vol.195 , pp. 471-496
    • Malaguti, L.1    Marcelli, C.2
  • 18
    • 0043133850 scopus 로고    scopus 로고
    • Travelling wave solutions of the degenerate Kolmogorov-Petrovski-Piskunov equation
    • G.S. Medvedev, K. Ono and P.J. Holmes, Travelling wave solutions of the degenerate Kolmogorov-Petrovski-Piskunov equation, Euro. Journal of Applied Mathematics 14 (2003), 343-367.
    • (2003) Euro. Journal of Applied Mathematics , vol.14 , pp. 343-367
    • Medvedev, G.S.1    Ono, K.2    Holmes, P.J.3
  • 19
    • 0018944419 scopus 로고
    • Some exact solutions to a nonlinear diffusion problem in population genetics and combustion
    • W.I. Newman, Some exact solutions to a nonlinear diffusion problem in population genetics and combustion, J. Theor. Biol. 85 (1980), 325-334.
    • (1980) J. Theor. Biol. , vol.85 , pp. 325-334
    • Newman, W.I.1
  • 20
    • 0001217997 scopus 로고
    • The Cauchy problem and boundary problems for equations of the type of nonstationary filtration
    • O.A. Oleinik, A.S. Kalashnikov and Y.-L. Chzhou, The Cauchy problem and boundary problems for equations of the type of nonstationary filtration (in Russian), Izv. Akad. Nauk. SSSR Ser. Mat. 22 (1958), 667-704.
    • (1958) Izv. Akad. Nauk. SSSR Ser. Mat. , vol.22 , pp. 667-704
    • Oleinik, O.A.1    Kalashnikov, A.S.2    Chzhou, Y.-L.3
  • 21
    • 84990623226 scopus 로고
    • 1 stability of travelling waves with applications to connective porous media flow
    • 1 stability of travelling waves with applications to connective porous media flow, Commun. Pure Appl. Math. 35 (1982), 737-749.
    • (1982) Commun. Pure Appl. Math. , vol.35 , pp. 737-749
    • Osher, S.1    Raison, J.2
  • 22
    • 4644306490 scopus 로고    scopus 로고
    • Singular solutions of doubly singular parabolic equations with absorption
    • Y. Qi and M. Wang, Singular solutions of doubly singular parabolic equations with absorption, Elect. J. Diff. Eq. 67 (2000), 1-22.
    • (2000) Elect. J. Diff. Eq. , vol.67 , pp. 1-22
    • Qi, Y.1    Wang, M.2
  • 23
    • 0037071294 scopus 로고    scopus 로고
    • Reaction and concentration dependent diffusion model
    • P. Rosenau, Reaction and concentration dependent diffusion model, Phy. Rev. Let. 88 (2002), 194501-4.
    • (2002) Phy. Rev. Let. , vol.88 , pp. 194501-194504
    • Rosenau, P.1
  • 24
    • 0000169258 scopus 로고
    • Travelling wave phenomena in some degenerate reaction-diffusion equations
    • F. Sánchez-Garduño and P.K. Maini, Travelling wave phenomena in some degenerate reaction-diffusion equations, J. Diff. Eq. 117 (1995), 281-319.
    • (1995) J. Diff. Eq. , vol.117 , pp. 281-319
    • Sánchez-Garduño, F.1    Maini, P.K.2
  • 26
    • 0000027176 scopus 로고
    • The behaviour of solutions of some nonlinear diffusion equations for large time
    • K. Uchiyama, The behaviour of solutions of some nonlinear diffusion equations for large time, J. Math. Kyoto Univ. 18 (1978), 453-508.
    • (1978) J. Math. Kyoto Univ. , vol.18 , pp. 453-508
    • Uchiyama, K.1
  • 27
    • 0000383614 scopus 로고
    • An introduction to the mathematical theory of the porous medium equation
    • Kluwer Acad. Publ., Dodrecht
    • J.L. Vazquez, An introduction to the mathematical theory of the porous medium equation, Shape Optimization, and Free Boundaries, Kluwer Acad. Publ., Dodrecht, 1992, 347-389.
    • (1992) Shape Optimization, and Free Boundaries , pp. 347-389
    • Vazquez, J.L.1
  • 29
    • 0041585659 scopus 로고    scopus 로고
    • On propagation of waves described by nonlinear parabolic equations
    • O.A. Oleinik (ed.), Translated by G.A. Yosifian, Gordon and Breach Publishers
    • A.I. Volpert, On propagation of waves described by nonlinear parabolic equations, in O.A. Oleinik (ed.), I.G. Petrowsky Selected Works, Part II. Differential Equations and Probability Theory, Translated by G.A. Yosifian, Gordon and Breach Publishers, 1996.
    • (1996) I.G. Petrowsky Selected Works, Part II. Differential Equations and Probability Theory
    • Volpert, A.I.1
  • 30
    • 0001412912 scopus 로고
    • Travelling wave solutions of parabolic systems
    • American Mathematical Society, Providence, Rhode Island, translated by James F. Heyda from an original Russian manuscript
    • A.I. Volpert, Vi.A. Volpert and Vl.A. Volpert, Travelling wave solutions of parabolic systems, American Mathematical Society, Providence, Rhode Island, 1994, Translation of Mathematical Monographs, vol. 140, translated by James F. Heyda from an original Russian manuscript.
    • (1994) Translation of Mathematical Monographs , vol.140
    • Volpert, A.I.1    Volpert, Vl.A.2    Volpert, Vl.A.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.