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Volumn 180, Issue 1, 2006, Pages 127-149

Intermediate asymptotics homogeneity and self-similarity: Long time behavior for u t = Δφ(u)

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EID: 31744450212     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00205-005-0403-4     Document Type: Article
Times cited : (22)

References (38)
  • 1
    • 31744435328 scopus 로고    scopus 로고
    • Existence of solutions to degenerate parabolic equations via the mongekantorovich theory
    • AGUEH, M.: Existence of solutions to degenerate parabolic equations via the mongekantorovich theory. Adv. Differential Equations. 10, 309-360 (2005)
    • (2005) Adv. Differential Equations. , vol.10 , pp. 309-360
    • Agueh, M.1
  • 4
    • 1642263787 scopus 로고    scopus 로고
    • Nonlinear diffusion and image contour enhancement
    • BARENBLATT, G.I., VÁZQUEZ, J.L.: Nonlinear diffusion and image contour enhancement. Interfaces Free Bound. 6, 31-54 (2004)
    • (2004) Interfaces Free Bound. , vol.6 , pp. 31-54
    • Barenblatt, G.I.1    Vázquez, J.L.2
  • 8
    • 0348037323 scopus 로고
    • The asymptotic profile of solutions of degenerate diffusion equations
    • BERTSCH, M., PELETIER, L.A.: The asymptotic profile of solutions of degenerate diffusion equations. Arch. Ration. Mech. Anal. 91, 207-229 (1985)
    • (1985) Arch. Ration. Mech. Anal. , vol.91 , pp. 207-229
    • Bertsch, M.1    Peletier, L.A.2
  • 11
    • 0037821662 scopus 로고    scopus 로고
    • Constrained steepest descent in the 2-wasserstein metric
    • CARLEN, E., GANGBO, W.: Constrained steepest descent in the 2-wasserstein metric. Ann. of Math. (2) 157, 807-846 (2003)
    • (2003) Ann. of Math. (2) , vol.157 , pp. 807-846
    • Carlen, E.1    Gangbo, W.2
  • 12
    • 17044380654 scopus 로고    scopus 로고
    • Long-time asymptotics via entropy methods for diffusion dominated equations
    • CARRILLO, J.A., FELLNER, K.: Long-time asymptotics via entropy methods for diffusion dominated equations. Asymptot. Anal. 42, 29-54 (2005)
    • (2005) Asymptot. Anal. , vol.42 , pp. 29-54
    • Carrillo, J.A.1    Fellner, K.2
  • 13
    • 18044401055 scopus 로고    scopus 로고
    • Entropy dissipation methods for degenerate parabolic problems and generalized sobolev inequalities
    • CARRILLO, J.A., JÜNGEL, A., MARKOWICH, P.A., TOSCANI, G., UNTERREITER, A.: Entropy dissipation methods for degenerate parabolic problems and generalized sobolev inequalities. Monatsh. Math. 133, 1-82 (2001)
    • (2001) Monatsh. Math. , vol.133 , pp. 1-82
    • Carrillo, J.A.1    Jüngel, A.2    Markowich, P.A.3    Toscani, G.4    Unterreiter, A.5
  • 14
    • 1542399709 scopus 로고    scopus 로고
    • Kinetic equilibration rates for granular media and related equations: Entropy dissipation and mass transportation estimates
    • CARRILLO, J.A., MCCANN, R.J., VILLANI, C.: Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates. Rev. Mat. Iberoamericana. 19, 1-48 (2003)
    • (2003) Rev. Mat. Iberoamericana. , vol.19 , pp. 1-48
    • Carrillo, J.A.1    Mccann, R.J.2    Villani, C.3
  • 15
    • 84920441804 scopus 로고    scopus 로고
    • Contractions in the 2-wasserstein length space and thermalization of granular media
    • To appear in
    • CARRILLO, J.A., MCCANN, R.J., VILLANI, C.: Contractions in the 2-wasserstein length space and thermalization of granular media. To appear in Arch. Ration. Mech. Anal.
    • Arch. Ration. Mech. Anal.
    • Carrillo, J.A.1    Mccann, R.J.2    Villani, C.3
  • 16
    • 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, 113-141 (2000)
    • (2000) Indiana Univ. Math. J. , vol.49 , pp. 113-141
    • Carrillo, J.A.1    Toscani, G.2
  • 19
    • 32544445405 scopus 로고    scopus 로고
    • Inequalities for generalized entropy and optimal transportation. Recent advances in the theory and applications of mass transport, 73-94
    • Amer. Math. Soc., Providence, RI
    • CORDERO-ERASQUIN, D., GANGBO, W., HOUDRÉ, C.: Inequalities for generalized entropy and optimal transportation. Recent advances in the theory and applications of mass transport, 73-94. Contemp. Math. 353, Amer. Math. Soc., Providence, RI, 2004
    • (2004) Contemp. Math. , vol.353
    • Cordero-Erasquin, D.1    Gangbo, W.2    Houdré, C.3
  • 21
    • 0036710614 scopus 로고    scopus 로고
    • Best constants for gagliardo-nirenberg inequalities and application to nonlinear diffusions
    • DOLBEAULT, J., DEL PINO, M.: Best constants for gagliardo-nirenberg inequalities and application to nonlinear diffusions. J. Math. Pures Appl. 81, 847-875 (2002)
    • (2002) J. Math. Pures Appl. , vol.81 , pp. 847-875
    • Dolbeault, J.1    Del Pino, M.2
  • 22
    • 84862599035 scopus 로고
    • Some problems of the qualitative theory of second-order nonlinear degenerate parabolic equations
    • KALASHNIKOV, A. S.: Some problems of the qualitative theory of second-order nonlinear degenerate parabolic equations. Russian Math. Surveys. 42, 169-222 (1987)
    • (1987) Russian Math. Surveys. , vol.42 , pp. 169-222
    • Kalashnikov, A.S.1
  • 23
    • 0016900774 scopus 로고
    • Similar solutions and the asymptotics of filtration equations
    • KAMIN, S.: Similar solutions and the asymptotics of filtration equations. Arch. Ration. Mech. Anal. 60, 171-183 (1975)
    • (1975) Arch. Ration. Mech. Anal. , vol.60 , pp. 171-183
    • Kamin, S.1
  • 24
    • 0012923806 scopus 로고
    • Some estimates for solution of the Cauchy problem for equations of a non-stationary filtration
    • KAMIN, S.: Some estimates for solution of the Cauchy problem for equations of a non-stationary filtration. J. Differential Equations. 20, 321-335 (1976)
    • (1976) J. Differential Equations. , vol.20 , pp. 321-335
    • Kamin, S.1
  • 25
    • 84968487166 scopus 로고
    • The porous medium equation in one dimension
    • KNERR, B.F.: The porous medium equation in one dimension. Trans. Amer. Math. Soc. 234, 381-415 (1977)
    • (1977) Trans. Amer. Math. Soc. , vol.234 , pp. 381-415
    • Knerr, B.F.1
  • 26
    • 0031161793 scopus 로고    scopus 로고
    • A convexity principle for interacting gases
    • MCCANN, R.J.: A convexity principle for interacting gases. Adv. Math. 128, 153-179 (1997)
    • (1997) Adv. Math. , vol.128 , pp. 153-179
    • Mccann, R.J.1
  • 27
    • 31744444524 scopus 로고    scopus 로고
    • Pims thematic programme on aymptotic geometric analysis: Concentration period on measure transportation and geometric inequalities
    • MCCANN, R.J.: Nonlinear diffusion to self-similarity: spreading versus shape via gradient flow. Pims thematic programme on aymptotic geometric analysis: Concentration period on measure transportation and geometric inequalities http://www.pims.math.ca, 2002.
    • (2002) Nonlinear Diffusion to Self-similarity: Spreading Versus Shape via Gradient Flow
    • Mccann, R.J.1
  • 28
    • 0001560970 scopus 로고    scopus 로고
    • The geometry of dissipative evolution equation: The porous medium equation
    • OTTO, F.: The geometry of dissipative evolution equation: the porous medium equation. Comm. Partial Differential Equations. 26, 101-174 (2001)
    • (2001) Comm. Partial Differential Equations , vol.26 , pp. 101-174
    • Otto, F.1
  • 29
    • 33746121129 scopus 로고    scopus 로고
    • Eulerian calculus for the contraction in the wasserstein distance
    • To appear in
    • OTTO, F., WESTDICKENBERG, M.: Eulerian calculus for the contraction in the wasserstein distance. To appear in SIAM J. Math. Anal.
    • SIAM J. Math. Anal.
    • Otto, F.1    Westdickenberg, M.2
  • 30
    • 12944272538 scopus 로고    scopus 로고
    • Convex functionals of probability measures and nonlinear diffusions on manifolds
    • To appear in
    • STURM, K.T.: Convex functionals of probability measures and nonlinear diffusions on manifolds. To appear in J. Math. Pures Appl.
    • J. Math. Pures Appl.
    • Sturm, K.T.1
  • 31
    • 3042573547 scopus 로고    scopus 로고
    • Kinetic and hydrodynamical models of nearly elastic granular flows
    • TOSCANI, G.: Kinetic and hydrodynamical models of nearly elastic granular flows. Monatsh. Math. 142, 179-192 (2004)
    • (2004) Monatsh. Math. , vol.142 , pp. 179-192
    • Toscani, G.1
  • 32
    • 20844460015 scopus 로고    scopus 로고
    • A central limit theorem for solutions of the porous medium equation
    • TOSCANI, G.: A central limit theorem for solutions of the porous medium equation. J. Evol. Equ. 5, 185-203 (2005)
    • (2005) J. Evol. Equ. , vol.5 , pp. 185-203
    • Toscani, G.1
  • 33
    • 0001421035 scopus 로고
    • A class of similarity solutions of the nonlinear diffusion equation
    • VAN DUYN, C.J., PELETIER, L.A.: A class of similarity solutions of the nonlinear diffusion equation. Nonlinear Anal. 1, 223-233 (1976/77)
    • (1976) Nonlinear Anal. , vol.1 , pp. 223-233
    • Van Duyn, C.J.1    Peletier, L.A.2
  • 34
    • 84962767376 scopus 로고
    • Asymptotic behaviour and propagation properties of the one-dimensional flow of gas in a porous medium
    • VÁZQUEZ, J.L.: Asymptotic behaviour and propagation properties of the one-dimensional flow of gas in a porous medium. Trans. Amer. Math. Soc. 277, 507-527 (1983)
    • (1983) Trans. Amer. Math. Soc. , vol.277 , pp. 507-527
    • Vázquez, J.L.1
  • 35
    • 0000383614 scopus 로고
    • An introduction to the mathematical theory of the porous medium equation, Shape optimization and free boundaries
    • Montreal, PQ. Kluwer Acad. Publ., Dordrecht
    • VÁZQUEZ, J.L.: An introduction to the mathematical theory of the porous medium equation, Shape optimization and free boundaries (Montreal, PQ, 1990). NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. vol. 380. Kluwer Acad. Publ., Dordrecht, 1992, 347-389
    • (1990) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. , vol.380 , pp. 347-389
    • Vázquez, J.L.1
  • 36
    • 0037847744 scopus 로고    scopus 로고
    • Asymptotic behaviour for the porous medium equation posed in the whole space
    • VÁZQUEZ, J.L.: Asymptotic behaviour for the porous medium equation posed in the whole space. J. Evol. Equ. 3, 67-118 (2003)
    • (2003) J. Evol. Equ. , vol.3 , pp. 67-118
    • Vázquez, J.L.1
  • 37
    • 0000399597 scopus 로고
    • Effets régularisants de semi-groupes non linéaires dans des espaces de Banach
    • VÉRON, L.: Effets régularisants de semi-groupes non linéaires dans des espaces de Banach. Ann. Fac. Sci. Toulouse Math. (5) 1, 171-200 (1979)
    • (1979) Ann. Fac. Sci. Toulouse Math. (5) , vol.1 , pp. 171-200
    • Véron, L.1
  • 38
    • 1542342359 scopus 로고    scopus 로고
    • Topics in optimal transportation
    • American Mathematical Society, Providence, RI
    • VILLANI, C.: Topics in optimal transportation. Graduate Studies in Mathematics. 58. American Mathematical Society, Providence, RI, 2003
    • (2003) Graduate Studies in Mathematics , vol.58
    • Villani, C.1


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