메뉴 건너뛰기




Volumn 42, Issue 1-2, 2005, Pages 29-54

Long-time asymptotics via entropy methods for diffusion dominated equations

Author keywords

Absorption diffusion; Convection diffusion; Convergence rate; Entropy methods; Large time behaviour

Indexed keywords

ABSORPTION; COMPUTATION THEORY; DIFFUSION; ENTROPY; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS;

EID: 17044380654     PISSN: 09217134     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (14)

References (34)
  • 1
    • 0042376716 scopus 로고    scopus 로고
    • On a parabolic equation with slow and fast diffusions
    • Ph. Bénilan and J.E. Bouillet, On a parabolic equation with slow and fast diffusions, Nonlinear Anal. 26 (1996), 813-822.
    • (1996) Nonlinear Anal. , vol.26 , pp. 813-822
    • Bénilan, Ph.1    Bouillet, J.E.2
  • 3
    • 84974004482 scopus 로고
    • Optimal smoothing and decay estimates for viscously damped conservation laws, with applications to the 2-D Navier-Stokes equation
    • E. Carlen and M. Loss, Optimal smoothing and decay estimates for viscously damped conservation laws, with applications to the 2-D Navier-Stokes equation, Duke Math. J. 81(1) (1995), 135-157.
    • (1995) Duke Math. J. , vol.81 , Issue.1 , pp. 135-157
    • Carlen, E.1    Loss, M.2
  • 4
    • 2342425267 scopus 로고    scopus 로고
    • Finite speed of propagation in porous media by mass transportation methods
    • J.A. Carrillo, M.P. Gualdani and G. Toscani, Finite speed of propagation in porous media by mass transportation methods, C. R. Acad. Sci. Paris 338(10) (2004), 815-818.
    • (2004) C. R. Acad. Sci. Paris , vol.338 , Issue.10 , pp. 815-818
    • Carrillo, J.A.1    Gualdani, M.P.2    Toscani, G.3
  • 5
    • 18044401055 scopus 로고    scopus 로고
    • Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities
    • J.A. Carrillo, A. Jüngel, P.A. Markowich, G. Toscani and A. Unterreiter, Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities, Monatsh. Math. 133 (2001), 1-81.
    • (2001) Monatsh. Math. , vol.133 , pp. 1-81
    • Carrillo, J.A.1    Jüngel, A.2    Markowich, P.A.3    Toscani, G.4    Unterreiter, A.5
  • 6
    • 0003277699 scopus 로고    scopus 로고
    • 1-decay of solutions of the porous medium equation to self-similarity
    • 1-decay of solutions of the porous medium equation to self-similarity, Indiana Univ. Math J. 49 (2000), 113-141.
    • (2000) Indiana Univ. Math J. , vol.49 , pp. 113-141
    • Carrillo, J.A.1    Toscani, G.2
  • 7
    • 17044414796 scopus 로고    scopus 로고
    • Wasserstein metric and large-time asymptotics of nonlinear diffusion equations
    • In Honour of the Salvatore Rionero 70th Birthday
    • J.A. Carrillo and G. Toscani, Wasserstein metric and large-time asymptotics of nonlinear diffusion equations, New Trends in Mathematical Physics (In Honour of the Salvatore Rionero 70th Birthday), 2005.
    • (2005) New Trends in Mathematical Physics
    • Carrillo, J.A.1    Toscani, G.2
  • 8
    • 0002449197 scopus 로고
    • Continuity of weak solutions to a general porous medium equation
    • E. DiBenedetto, Continuity of weak solutions to a general porous medium equation, Indiana Math. Univ. J. 32 (1983), 83-118.
    • (1983) Indiana Math. Univ. J. , vol.32 , pp. 83-118
    • Dibenedetto, E.1
  • 9
    • 17044375749 scopus 로고    scopus 로고
    • Entropy dissipation and Wasserstein metric methods for the viscous Burgers' equation: Convergence to diffusive waves
    • Contemp. Math., Amer. Math. Soc., Providence, RI
    • M. Di Francesco and P.A. Markowich, Entropy dissipation and Wasserstein metric methods for the viscous Burgers' equation: convergence to diffusive waves, in: Partial Differential Equations and Inverse Problems, Contemp. Math., Vol. 362, Amer. Math. Soc., Providence, RI, 2004, pp. 145-165.
    • (2004) Partial Differential Equations and Inverse Problems , vol.362 , pp. 145-165
    • Di Francesco, M.1    Markowich, P.A.2
  • 10
    • 14844347570 scopus 로고    scopus 로고
    • ∞ intermediate asymptotics for scalar conservation laws
    • ∞ intermediate asymptotics for scalar conservation laws, Asymptotic Analysis 41(3,4) (2005), 189-213.
    • (2005) Asymptotic Analysis , vol.41 , Issue.3-4 , pp. 189-213
    • Dolbeault, J.1    Escobedo, M.2
  • 11
    • 0036710614 scopus 로고    scopus 로고
    • Best constants for Gagliardo-Nirenberg inequalities and application to nonlinear diffusions
    • J. Dolbeault and M. del Pino, Best constants for Gagliardo-Nirenberg inequalities and application to nonlinear diffusions, J. Math. Pures Appl. 81(9) (2002), 847-875.
    • (2002) J. Math. Pures Appl. , vol.81 , Issue.9 , pp. 847-875
    • Dolbeault, J.1    Del Pino, M.2
  • 12
    • 0000194981 scopus 로고
    • Moments, masses de Dirac et décomposition de functions
    • J. Duoandikoetxea and E. Zuazua, Moments, masses de Dirac et décomposition de functions, C. R. Acad. Sci. Paris Ser. I Math. 315(6) (1992), 693-698.
    • (1992) C. R. Acad. Sci. Paris Ser. I Math. , vol.315 , Issue.6 , pp. 693-698
    • Duoandikoetxea, J.1    Zuazua, E.2
  • 14
    • 34250077986 scopus 로고
    • Asymptotic behaviour and source-type solutions for a diffusion-convection equations
    • M. Escobedo, J.L. Vázquez and J.L. Zuazua, Asymptotic behaviour and source-type solutions for a diffusion-convection equations, Arch. Rational Mech. Anal. 124 (1993), 43-65.
    • (1993) Arch. Rational Mech. Anal. , vol.124 , pp. 43-65
    • Escobedo, M.1    Vázquez, J.L.2    Zuazua, J.L.3
  • 15
    • 0002483505 scopus 로고
    • The occurrence of interfaces in nonlinear diffusion-advection processes
    • B.H. Gilding, The occurrence of interfaces in nonlinear diffusion-advection processes, Arch. Rational Mech. Anal. 100 (1988), 243-263.
    • (1988) Arch. Rational Mech. Anal. , vol.100 , pp. 243-263
    • Gilding, B.H.1
  • 16
    • 0001279719 scopus 로고
    • Improved theory for a nonlinear degenerate parabolic equation
    • B.H. Gilding, Improved theory for a nonlinear degenerate parabolic equation, Ann. Scuola Norm. Sup. Pisa (4) 16 (1989), 165-224.
    • (1989) Ann. Scuola Norm. Sup. Pisa , vol.16 , Issue.4 , pp. 165-224
    • Gilding, B.H.1
  • 18
    • 0000470675 scopus 로고
    • Asymptotic behaviour of nonlinear parabolic equations with critical exponents. a dynamial systems approach
    • V. Galaktionov and J. Vázquez, Asymptotic behaviour of nonlinear parabolic equations with critical exponents. A dynamial systems approach, J. Funct. Anal. 100(2) (1991), 435-462.
    • (1991) J. Funct. Anal. , vol.100 , Issue.2 , pp. 435-462
    • Galaktionov, V.1    Vázquez, J.2
  • 19
    • 0001166785 scopus 로고
    • The one-dimensional nonlinear heat equation with absorption: Regularity of solutions and interfaces
    • M. Herrero and J. Vázquez, The one-dimensional nonlinear heat equation with absorption: regularity of solutions and interfaces, SIAM J. Math. Anal. 18(1) (1987), 149-167.
    • (1987) SIAM J. Math. Anal. , vol.18 , Issue.1 , pp. 149-167
    • Herrero, M.1    Vázquez, J.2
  • 20
    • 0001018828 scopus 로고    scopus 로고
    • Source-type solutions to porous medium equations with convection
    • Ph. Laurençot and F. Simondon, Source-type solutions to porous medium equations with convection, Comm. Appl. Anal. 1 (1997), 489-502.
    • (1997) Comm. Appl. Anal. , vol.1 , pp. 489-502
    • Laurençot, Ph.1    Simondon, F.2
  • 21
    • 22044440316 scopus 로고    scopus 로고
    • Long-time behaviour for the porous medium equations with convection
    • Ph. Laurençot and F. Simondon, Long-time behaviour for the porous medium equations with convection, Proc. Roy. Soc. Edinburgh Sect. A 128 (1998), 315-336.
    • (1998) Proc. Roy. Soc. Edinburgh Sect. a , vol.128 , pp. 315-336
    • Laurençot, P.1    Simondon, F.2
  • 22
    • 0038811607 scopus 로고    scopus 로고
    • On fast-diffusion equations with infinite equilibrium entropy and finite equilibrium mass
    • C. Lederman and P.A. Markowich, On fast-diffusion equations with infinite equilibrium entropy and finite equilibrium mass, Comm. Partial Differential Equations 28(1-2) (2003), 301-332.
    • (2003) Comm. Partial Differential Equations , vol.28 , Issue.1-2 , pp. 301-332
    • Lederman, C.1    Markowich, P.A.2
  • 23
    • 3042676199 scopus 로고    scopus 로고
    • Long-time asymptotics of kinetic models of granular flows
    • H. Li and G. Toscani, Long-time asymptotics of kinetic models of granular flows, Arch. Rational Mech. Anal. 172(3) (2004), 407-428.
    • (2004) Arch. Rational Mech. Anal. , vol.172 , Issue.3 , pp. 407-428
    • Li, H.1    Toscani, G.2
  • 24
    • 0005516086 scopus 로고    scopus 로고
    • On solutions to nonlinear reaction-diffusion-convection equations with degenerate diffusion
    • Y. Lu and W. Jäger, On solutions to nonlinear reaction-diffusion- convection equations with degenerate diffusion, J. Differential Equations 170 (2001), 1-21.
    • (2001) J. Differential Equations , vol.170 , pp. 1-21
    • Lu, Y.1    Jäger, W.2
  • 25
    • 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. Surveys 42 (1987), 169-222.
    • (1987) Russian Math. Surveys , vol.42 , pp. 169-222
    • Kalashnikov, A.S.1
  • 26
    • 51249178019 scopus 로고
    • Large time behaviour of solutions of the porous media equation with absorption
    • S. Kamin and L.A. Peletier, Large time behaviour of solutions of the porous media equation with absorption, Israel J. Math. 55(2) (1986), 129-146.
    • (1986) Israel J. Math. , vol.55 , Issue.2 , pp. 129-146
    • Kamin, S.1    Peletier, L.A.2
  • 27
    • 0009332069 scopus 로고
    • A nonlinear diffusion-absorption equation with unbounded initial data
    • (Gregynog, 1989), Progr. Nonlinear Differential Equations Appl., Vol. 7, Birkhäuser, Boston
    • S. Kamin, L.A. Peletier and J. Vázquez, A nonlinear diffusion-absorption equation with unbounded initial data, in: Nonlinear Diffusion Equations and Their Equilibrium States, 3 (Gregynog, 1989), Progr. Nonlinear Differential Equations Appl., Vol. 7, Birkhäuser, Boston, 1992, pp. 243-263.
    • (1992) Nonlinear Diffusion Equations and Their Equilibrium States , vol.3 , pp. 243-263
    • Kamin, S.1    Peletier, L.A.2    Vázquez, J.3
  • 28
    • 0001560970 scopus 로고    scopus 로고
    • The geometry of dissipative evolution equations: The porous medium equation
    • F. Otto, The geometry of dissipative evolution equations: the porous medium equation, Comm. Partial Differential Equations 26 (2001), 101-174.
    • (2001) Comm. Partial Differential Equations , vol.26 , pp. 101-174
    • Otto, F.1
  • 29
    • 0033164465 scopus 로고    scopus 로고
    • Asymptotic behaviour in convection-diffusion processes
    • G. Reyes, Asymptotic behaviour in convection-diffusion processes, Nonlinear Anal. Ser. A: Theory Methods, 37(3) (1999), 301-318.
    • (1999) Nonlinear Anal. Ser. A: Theory Methods , vol.37 , Issue.3 , pp. 301-318
    • Reyes, G.1
  • 30
    • 0033147982 scopus 로고    scopus 로고
    • Asymptotic behaviour of a generalized Burgers' equation
    • G. Reyes and J.L. Vázquez, Asymptotic behaviour of a generalized Burgers' equation, J. Math. Pures Appl. 78 (1999), 633-666.
    • (1999) J. Math. Pures Appl. , vol.78 , pp. 633-666
    • Reyes, G.1    Vázquez, J.L.2
  • 31
    • 0000383614 scopus 로고
    • An introduction to the mathematical theory of the porous medium equation
    • (Montreal, PQ, 1990), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Kluwer-Academic
    • J.L. Vázquez, An introduction to the mathematical theory of the porous medium equation, in: Shape Optimization and Free Boundaries (Montreal, PQ, 1990), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Vol. 380, Kluwer-Academic, 1992, pp. 347-389.
    • (1992) Shape Optimization and Free Boundaries , vol.380 , pp. 347-389
    • Vázquez, J.L.1
  • 32
    • 17044414367 scopus 로고    scopus 로고
    • A priori estimates, Lagrangian coordinates and the regularity of nonlinear diffusion equations
    • J.L. Vázquez, A priori estimates, Lagrangian coordinates and the regularity of nonlinear diffusion equations, Rev. Un. Mat. Argentina 41(1) (1998), 115-128.
    • (1998) Rev. Un. Mat. Argentina , vol.41 , Issue.1 , pp. 115-128
    • Vázquez, J.L.1
  • 33
    • 2442557820 scopus 로고    scopus 로고
    • Graduate Studies in Mathematics, AMS ISSN: 1065-7339
    • C. Villani, Topics in Mass Transportation, Graduate Studies in Mathematics, Vol. 58, 2003, AMS ISSN: 1065-7339.
    • (2003) Topics in Mass Transportation , vol.58
    • Villani, C.1
  • 34
    • 84972496033 scopus 로고
    • Weakly nonlinear large time behavior in scalr convection-diffusion equations
    • E. Zuazua, Weakly nonlinear large time behavior in scalr convection-diffusion equations, Differential Integral Equations 6(6) (1993), 1481-1491.
    • (1993) Differential Integral Equations , vol.6 , Issue.6 , pp. 1481-1491
    • Zuazua, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.