메뉴 건너뛰기




Volumn 319, Issue 1, 2006, Pages 157-176

Exponential decay toward equilibrium via entropy methods for reaction-diffusion equations

Author keywords

Entropy method; Exponential decay; Reaction diffusion

Indexed keywords


EID: 33645548609     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2005.07.003     Document Type: Article
Times cited : (127)

References (45)
  • 1
    • 0002970101 scopus 로고
    • Global existence for semilinear parabolic problems
    • H. Amann Global existence for semilinear parabolic problems J. Reine Angew. Math. 360 1985 47-83
    • (1985) J. Reine Angew. Math. , vol.360 , pp. 47-83
    • Amann, H.1
  • 2
    • 0000209068 scopus 로고
    • On the global existence of solutions of a reaction-diffusion equation with exponential nonlinearity
    • A. Barabanova On the global existence of solutions of a reaction-diffusion equation with exponential nonlinearity Proc. Amer. Math. Soc. 122 1994 827-831
    • (1994) Proc. Amer. Math. Soc. , vol.122 , pp. 827-831
    • Barabanova, A.1
  • 3
    • 33751026682 scopus 로고    scopus 로고
    • From reactive Boltzmann equations to reaction-diffusion systems
    • preprint 2005-11 of the CMLA, ENS de Cachan
    • M. Bisi, L. Desvillettes, From reactive Boltzmann equations to reaction-diffusion systems, preprint 2005-11 of the CMLA, ENS de Cachan, 2005
    • (2005)
    • Bisi, M.1    Desvillettes, L.2
  • 4
    • 0142087796 scopus 로고    scopus 로고
    • A reaction-diffusion system with fast reversible reaction
    • D. Bothe D. Hilhorst A reaction-diffusion system with fast reversible reaction J. Math. Anal. Appl. 286 2003 125-135
    • (2003) J. Math. Anal. Appl. , vol.286 , pp. 125-135
    • Bothe, D.1    Hilhorst, D.2
  • 5
    • 14844333851 scopus 로고    scopus 로고
    • Long-time behavior for a nonlinear fourth order parabolic equation
    • (electronic)
    • M. Caceres J. Carrillo G. Toscani Long-time behavior for a nonlinear fourth order parabolic equation Trans. Amer. Math. Soc. 357 2005 1161-1175
    • (2005) Trans. Amer. Math. Soc. , vol.357 , pp. 1161-1175
    • Caceres, M.1    Carrillo, J.2    Toscani, G.3
  • 6
    • 0038381004 scopus 로고    scopus 로고
    • Equilibration rate for the linear inhomogeneous relaxation-time Boltzmann equation for charged particles
    • M. Caceres J. Carrillo T. Goudon Equilibration rate for the linear inhomogeneous relaxation-time Boltzmann equation for charged particles Comm. Partial Differential Equations 28 2003 969-989
    • (2003) Comm. Partial Differential Equations , vol.28 , pp. 969-989
    • Caceres, M.1    Carrillo, J.2    Goudon, T.3
  • 7
    • 0001842649 scopus 로고
    • Large time behaviour of solutions of systems of nonlinear reaction-diffusion equations
    • E. Conway D. Hoff J. Smoller Large time behaviour of solutions of systems of nonlinear reaction-diffusion equations SIAM J. Appl. Math. 35 1978 1-16
    • (1978) SIAM J. Appl. Math. , vol.35 , pp. 1-16
    • Conway, E.1    Hoff, D.2    Smoller, J.3
  • 8
    • 0001856347 scopus 로고
    • Eine informationstheoretische Ungleichung und ihre Anwendung auf den Beweis von Markoffschen Ketten
    • I. Csiszár Eine informationstheoretische Ungleichung und ihre Anwendung auf den Beweis von Markoffschen Ketten Magyar Tud. Akad. Mat. Kutató Int. Közl. 8 1963 85-108
    • (1963) Magyar Tud. Akad. Mat. Kutató Int. Közl. , vol.8 , pp. 85-108
    • Csiszár, I.1
  • 10
    • 0036710614 scopus 로고    scopus 로고
    • Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions
    • M. Del Pino J. Dolbeault Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions J. Math. Pures Appl. 81 2002 847-875
    • (2002) J. Math. Pures Appl. , vol.81 , pp. 847-875
    • Del Pino, M.1    Dolbeault, J.2
  • 12
    • 84893153516 scopus 로고    scopus 로고
    • Entropy methods for reaction-diffusion equations: Degenerate diffusion and slowly growing a-priori bounds
    • preprint HYKE2005-103, available at www.hyke.org
    • L. Desvillettes K. Fellner Entropy methods for reaction-diffusion equations: Degenerate diffusion and slowly growing a-priori bounds preprint HYKE2005-103, available at www.hyke.org
    • Desvillettes, L.1    Fellner, K.2
  • 13
    • 0000278899 scopus 로고    scopus 로고
    • On the spatially homogeneous Landau equation for hard potentials. II. H-theorem and applications
    • L. Desvillettes C. Villani On the spatially homogeneous Landau equation for hard potentials. II. H-theorem and applications Comm. Partial Differential Equations 25 2000 261-298
    • (2000) Comm. Partial Differential Equations , vol.25 , pp. 261-298
    • Desvillettes, L.1    Villani, C.2
  • 14
    • 0035526707 scopus 로고    scopus 로고
    • On the trend to global equilibrium in spatially inhomogeneous entropy-dissipating systems: The linear Fokker-Planck equation
    • L. Desvillettes C. Villani On the trend to global equilibrium in spatially inhomogeneous entropy-dissipating systems: The linear Fokker-Planck equation Comm. Pure Appl. Math. 54 2001 1-42
    • (2001) Comm. Pure Appl. Math. , vol.54 , pp. 1-42
    • Desvillettes, L.1    Villani, C.2
  • 15
    • 12844275468 scopus 로고    scopus 로고
    • On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation
    • L. Desvillettes C. Villani On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation Invent. Math. 159 2005 245-316
    • (2005) Invent. Math. , vol.159 , pp. 245-316
    • Desvillettes, L.1    Villani, C.2
  • 17
    • 2142838409 scopus 로고    scopus 로고
    • Convergence to global equilibrium for spatially inhomogeneous kinetic models of non-micro-reversible processes
    • K. Fellner L. Neumann C. Schmeiser Convergence to global equilibrium for spatially inhomogeneous kinetic models of non-micro-reversible processes Monatsh. Math. 141 2004 289-299
    • (2004) Monatsh. Math. , vol.141 , pp. 289-299
    • Fellner, K.1    Neumann, L.2    Schmeiser, C.3
  • 18
    • 0345932445 scopus 로고
    • Coupled system of reaction-diffusion equations and applications in carrier facilitated diffusion
    • W. Feng Coupled system of reaction-diffusion equations and applications in carrier facilitated diffusion Nonlinear Anal. 17 1991 285-311
    • (1991) Nonlinear Anal. , vol.17 , pp. 285-311
    • Feng, W.1
  • 19
    • 0003299218 scopus 로고
    • Mathematical Aspects of Reacting and Diffusing Systems
    • Springer Berlin
    • P.C. Fife Mathematical Aspects of Reacting and Diffusing Systems Lecture Notes in Biomath. vol. 28 1979 Springer Berlin
    • (1979) Lecture Notes in Biomath. , vol.28
    • Fife, P.C.1
  • 20
    • 38249008528 scopus 로고
    • Global existence and boundedness for a class of inhomogeneous semilinear parabolic systems
    • W.E. Fitzgibbon J. Morgan R. Sanders Global existence and boundedness for a class of inhomogeneous semilinear parabolic systems Nonlinear Anal. 19 1992 885-899
    • (1992) Nonlinear Anal. , vol.19 , pp. 885-899
    • Fitzgibbon, W.E.1    Morgan, J.2    Sanders, R.3
  • 21
    • 0031519867 scopus 로고    scopus 로고
    • Stability and Lyapunov functions for reaction-diffusion systems
    • W. Fitzgibbon S. Hollis J. Morgan Stability and Lyapunov functions for reaction-diffusion systems SIAM J. Math. Anal. 28 1997 595-610
    • (1997) SIAM J. Math. Anal. , vol.28 , pp. 595-610
    • Fitzgibbon, W.1    Hollis, S.2    Morgan, J.3
  • 22
    • 26544437650 scopus 로고
    • Free energy estimates and asymptotic behaviour of reaction-diffusion processes
    • preprint 20, Institut für Angewandte Analysis und Stochastik, Berlin
    • K. Gröger, Free energy estimates and asymptotic behaviour of reaction-diffusion processes, preprint 20, Institut für Angewandte Analysis und Stochastik, Berlin (1992)
    • (1992)
    • Gröger, K.1
  • 23
    • 0001150074 scopus 로고    scopus 로고
    • Free energy and dissipation rate for reaction-diffusion processes of electrically charged species
    • A. Glitzky K. Gröger R. Hünlich Free energy and dissipation rate for reaction-diffusion processes of electrically charged species Appl. Anal. 60 1996 201-217
    • (1996) Appl. Anal. , vol.60 , pp. 201-217
    • Glitzky, A.1    Gröger, K.2    Hünlich, R.3
  • 24
    • 21944454067 scopus 로고    scopus 로고
    • Energetic estimates and asymptotics for electro-reaction-diffusion systems
    • A. Glitzky R. Hünlich Energetic estimates and asymptotics for electro-reaction-diffusion systems Z. Angew. Math. Mech. 77 1997 823-832
    • (1997) Z. Angew. Math. Mech. , vol.77 , pp. 823-832
    • Glitzky, A.1    Hünlich, R.2
  • 25
    • 84972572538 scopus 로고
    • On a result of K. Masuda concerning reaction-diffusion equations
    • A. Haraux A. Youkana On a result of K. Masuda concerning reaction-diffusion equations Tôhoku Math. J. 4 1988 159-163
    • (1988) Tôhoku Math. J. , vol.4 , pp. 159-163
    • Haraux, A.1    Youkana, A.2
  • 26
    • 0001243397 scopus 로고
    • Global existence and boundedness in reaction-diffusion systems
    • S. Hollis R. Martin M. Pierre Global existence and boundedness in reaction-diffusion systems SIAM J. Math. Appl. 18 1987 744-761
    • (1987) SIAM J. Math. Appl. , vol.18 , pp. 744-761
    • Hollis, S.1    Martin, R.2    Pierre, M.3
  • 27
    • 0039552866 scopus 로고
    • Asymptotic behavior of global solutions for some reaction-diffusion systems
    • H. Hoshino Y. Yamada Asymptotic behavior of global solutions for some reaction-diffusion systems Nonlinear Anal. 23 1994 639-650
    • (1994) Nonlinear Anal. , vol.23 , pp. 639-650
    • Hoshino, H.1    Yamada, Y.2
  • 28
    • 0009345577 scopus 로고
    • Cauchy's problem for semilinear parabolic equations with balance conditions
    • English transl.:
    • Y.I. Kanel Cauchy's problem for semilinear parabolic equations with balance conditions Differ. Uravn. 20 1984 1753-1760
    • (1984) Differ. Uravn. , vol.20 , pp. 1753-1760
    • Kanel, Y.I.1
  • 29
    • 0034691385 scopus 로고    scopus 로고
    • Global solutions of reaction-diffusion systems with a balance law and nonlinearities of exponential growth
    • Y.I. Kanel M. Kirane Global solutions of reaction-diffusion systems with a balance law and nonlinearities of exponential growth J. Differential Equations 165 2000 24-41
    • (2000) J. Differential Equations , vol.165 , pp. 24-41
    • Kanel, Y.I.1    Kirane, M.2
  • 30
    • 33645535361 scopus 로고
    • On stabilization of solutions of the system of parabolic differential equations describing the kinetics of an autocatalytic reversible chemical reaction
    • M. Kirane On stabilization of solutions of the system of parabolic differential equations describing the kinetics of an autocatalytic reversible chemical reaction Bull. Inst. Mat. Acad. Sinica 18 1990 369-377
    • (1990) Bull. Inst. Mat. Acad. Sinica , vol.18 , pp. 369-377
    • Kirane, M.1
  • 32
    • 33645553238 scopus 로고
    • Nonlinear Equations in Applied Sciences
    • Academic Press New York
    • R.H. Martin M. Pierre Nonlinear reaction-diffusion systems W.F. Ames C. Rogers Nonlinear Equations in Applied Sciences Math. Sci. Eng. vol. 185 1991 Academic Press New York
    • (1991) Math. Sci. Eng. , vol.185
    • Martin, R.H.1    Pierre, M.2
  • 33
    • 0001543307 scopus 로고
    • On the global existence and asymptotic behavior of solution of reaction-diffusion equations
    • K. Masuda On the global existence and asymptotic behavior of solution of reaction-diffusion equations Hokkaido Math. J. 12 1983 360-370
    • (1983) Hokkaido Math. J. , vol.12 , pp. 360-370
    • Masuda, K.1
  • 34
    • 0000753609 scopus 로고
    • Global existence for semilinear parabolic systems
    • J. Morgan Global existence for semilinear parabolic systems SIAM J. Math. Anal. 20 1989 1128-1144
    • (1989) SIAM J. Math. Anal. , vol.20 , pp. 1128-1144
    • Morgan, J.1
  • 35
    • 0003568123 scopus 로고
    • Global Solutions of Reaction-Diffusion Systems
    • Springer Berlin
    • F. Rothe Global Solutions of Reaction-Diffusion Systems Lecture Notes in Math. 1984 Springer Berlin
    • (1984) Lecture Notes in Math.
    • Rothe, F.1
  • 36
    • 0003233281 scopus 로고
    • Shock Waves and Reaction-Diffusion Equations
    • Springer New York
    • J. Smoller Shock Waves and Reaction-Diffusion Equations Grundlehren Math. Wiss. vol. 258 1983 Springer New York
    • (1983) Grundlehren Math. Wiss. , vol.258
    • Smoller, J.1
  • 37
    • 33645543620 scopus 로고
    • Reaction-diffusion models from the Fokker-Planck formulation of chemical processes
    • R. Spigler D.H. Zanette Reaction-diffusion models from the Fokker-Planck formulation of chemical processes IMA J. Appl. Math. 49 1992 217-229
    • (1992) IMA J. Appl. Math. , vol.49 , pp. 217-229
    • Spigler, R.1    Zanette, D.H.2
  • 38
    • 33645552828 scopus 로고
    • A BGK model for chemical processes: The reaction-diffusion approximation
    • R. Spigler D.H. Zanette A BGK model for chemical processes: The reaction-diffusion approximation Math. Models Methods Appl. Sci. 4 1994 35-47
    • (1994) Math. Models Methods Appl. Sci. , vol.4 , pp. 35-47
    • Spigler, R.1    Zanette, D.H.2
  • 39
    • 84990617545 scopus 로고
    • Propagation of chaos for a system of annihilating Brownian spheres
    • A.-S. Sznitman Propagation of chaos for a system of annihilating Brownian spheres Comm. Pure Appl. Math. 40 1987 663-690
    • (1987) Comm. Pure Appl. Math. , vol.40 , pp. 663-690
    • Sznitman, A.-S.1
  • 40
    • 0033242961 scopus 로고    scopus 로고
    • Sharp entropy dissipation bounds and explicit rate of trend to equilibrium for the spatially homogeneous Boltzmann equation
    • G. Toscani C. Villani Sharp entropy dissipation bounds and explicit rate of trend to equilibrium for the spatially homogeneous Boltzmann equation Comm. Math. Phys. 203 1999 667-706
    • (1999) Comm. Math. Phys. , vol.203 , pp. 667-706
    • Toscani, G.1    Villani, C.2
  • 41
    • 0034147246 scopus 로고    scopus 로고
    • On the trend to equilibrium for some dissipative systems with slowly increasing a priori bounds
    • G. Toscani C. Villani On the trend to equilibrium for some dissipative systems with slowly increasing a priori bounds J. Statist. Phys. 98 2000 1279-1309
    • (2000) J. Statist. Phys. , vol.98 , pp. 1279-1309
    • Toscani, G.1    Villani, C.2
  • 42
    • 0037358153 scopus 로고    scopus 로고
    • Cercignani's conjecture is sometimes true and always almost true
    • C. Villani Cercignani's conjecture is sometimes true and always almost true Comm. Math. Phys. 234 2003 455-490
    • (2003) Comm. Math. Phys. , vol.234 , pp. 455-490
    • Villani, C.1
  • 43
    • 0001412911 scopus 로고
    • Traveling Wave Solutions of Parabolic Systems
    • Amer. Math. Soc. Providence, RI
    • A. Volpert V.A. Volpert V.A. Volpert Traveling Wave Solutions of Parabolic Systems Transl. Math. Monogr. vol. 140 1994 Amer. Math. Soc. Providence, RI
    • (1994) Transl. Math. Monogr. , vol.140
    • Volpert, A.1    Volpert, V.A.2    Volpert, V.A.3
  • 44
    • 0003281481 scopus 로고
    • Theory of Nonlinear Age-Dependent Population Dynamics
    • Dekker New York
    • G.F. Webb Theory of Nonlinear Age-Dependent Population Dynamics Monogr. Textbooks Pure Appl. Math. vol. 89 1985 Dekker New York
    • (1985) Monogr. Textbooks Pure Appl. Math. , vol.89
    • Webb, G.F.1
  • 45
    • 0001883856 scopus 로고
    • Stabilization of solutions to boundary value problems for second order parabolic equations in one space variable
    • T. Zelenyak Stabilization of solutions to boundary value problems for second order parabolic equations in one space variable Differ. Uravn. 4 1968 34-45
    • (1968) Differ. Uravn. , vol.4 , pp. 34-45
    • Zelenyak, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.