Asymptotic behaviour of nonlinear parabolic equations with critical exponents. A dynamical systems approach

Aronson, 1979, Régularité des solutions de l'équation des milieux poreux dans RN, C. R. Acad. Sci. Paris Sér. 1, 288, 103

Bénilan, 1976, Opérateurs accrétifs et semigroupes dans les espaces Lp (1 ⩽ p ⩽ ∞)

Brezis, 1983, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pures Appl., 62, 73

Di Benedetto, 1983, Continuity of weak solutions to a general porous medium equation, Indiana Univ. Math. J., 32, 83, 10.1512/iumj.1983.32.32008

Di Benedetto, 1986, A boundary modulus of continuity of a class of singular parabolic equations, J. Differential Equations, 63, 418, 10.1016/0022-0396(86)90064-1

Bénilan, 1981, The continuous dependence on φ of solutions of ut = Δφ(u), Indiana Univ. Math. J., 30, 161, 10.1512/iumj.1981.30.30014

Esteban, 1988, A nonlinear heat equation with singular diffusivity, Comm. Partial Differential Equations, 13, 985, 10.1080/03605308808820566

Friedman, 1980, The asymptotic behavior of gas in an n-dimensional porous medium, Trans. Amer. Math. Soc., 262, 551

Galaktionov, 1985, On the asymptotic “eigenfunctions” of the Cauchy problem for some nonlinear parabolic equation, Mat. Sb., 126, 435

Galaktionov, 1986, Asymptotics of nonlinear heat conduction with absorption under the critical exponent

Gmira, 1984, Large time behaviour of solutions of a semilinear problem in RN, J. Differential Equations, 53, 258, 10.1016/0022-0396(84)90042-1

Kalashnikov, 1974, On the propagation of disturbances in problems of nonlinear heat conduction with absorption, J. Vichisl. Mat. i Mat. Fiz., 14, 891

Kalashnikov, 1987, Some questions on the qualitative theory of nonlinear degenerate second-order equations, Uspekhi Mat. Nauk, 42, 135

Kamin, 1985, Large time behaviour of the heat equation with absorption, Ann. Scuola Norm. Sup. Pisa, 12, 393

Kamin, 1986, Large time behaviour of solutions of the porous media equation with absorption, Israel J. Math., 55, 129, 10.1007/BF02801989

Kamin, 1989, Classification of singular solutions of a nonlinear heat equation, Duke Math. J., 58, 601, 10.1215/S0012-7094-89-05828-6

Kamin, 1987, On the behaviour as t → ∞ of the solutions of the Cauchy problem for certain nonlinear parabolic equations, J. Math. Anal. Appl., 128, 456, 10.1016/0022-247X(87)90196-X

Kamin, 1988, Fundamental solutions and asymptotic behaviour for the p-Laplacian equation, Rev. Mat. Iberoamericana, 4, 339, 10.4171/RMI/77

Kamin, 1991, Asymptotic behaviour of solutions of the porous medium equation with changing sign, SIAM J. Math. Anal., 22, 34, 10.1137/0522003

Kersner, 1978, On some properties of weak solutions to quasilinear degenerate parabolic equations, Acta Math. Acad. Sci. Hungar., 32, 301

Peletier, 1986, A very singular solution of the porous media equation with absorption, J. Differential Equations, 65, 396, 10.1016/0022-0396(86)90026-4

Samarskii, 1987

Véron, 1979, Effects régularisants des semi-groupes non linéaires dans les espaces de Banach, Ann. Fac. Sci. Toulouse, 1, 171, 10.5802/afst.535