Blow-up and global existence profile of a class of fully nonlinear degenerate parabolic equations

Jing Li; Jingxue Yin; Chunhua Jin

Displaying similar documents to “Blow-up and global existence profile of a class of fully nonlinear degenerate parabolic equations”

A remark on the uniqueness of fundamental solutions to the $p$ -Laplacian equation, $p > 2$ .

Laurençot, Ph. (1998)

Portugaliae Mathematica

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Hardy inequalities and dynamic instability of singular Yamabe metrics

Adriano Pisante (2006)

Annales de l'I.H.P. Analyse non linéaire

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Large time behavior of solutions to a class of doubly nonlinear parabolic equations

Hua Shui Zhan (2008)

Applications of Mathematics

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We study the large time asymptotic behavior of solutions of the doubly degenerate parabolic equation $u_{t} = div (u^{m - 1} {| D u |}^{p - 2} D u) - u^{q}$ with an initial condition $u (x, 0) = u_{0} (x)$ . Here the exponents $m$ , $p$ and $q$ satisfy $m + p \geq 3$ , $p > 1$ and $q > m + p - 2$ .

Regularity and uniqueness in quasilinear parabolic systems

Pavel Krejčí, Lucia Panizzi (2011)

Applications of Mathematics

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Inspired by a problem in steel metallurgy, we prove the existence, regularity, uniqueness, and continuous data dependence of solutions to a coupled parabolic system in a smooth bounded 3D domain, with nonlinear and nonhomogeneous boundary conditions. The nonlinear coupling takes place in the diffusion coefficient. The proofs are based on anisotropic estimates in tangential and normal directions, and on a refined variant of the Gronwall lemma.

A note on the Cahn-Hilliard equation in $H^{1} (ℝ^{N})$ involving critical exponent

Jan W. Cholewa, Aníbal Rodríguez-Bernal (2014)

Mathematica Bohemica

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We consider the Cahn-Hilliard equation in $H^{1} (ℝ^{N})$ with two types of critically growing nonlinearities: nonlinearities satisfying a certain limit condition as $| u | \to \infty$ and logistic type nonlinearities. In both situations we prove the $H^{2} (ℝ^{N})$ -bound on the solutions and show that the individual solutions are suitably attracted by the set of equilibria. This complements the results in the literature; see J. W. Cholewa, A. Rodriguez-Bernal (2012).

Existence and asymptotic behaviour of positive solutions for some nonlinear parabolic systems in the half-space.

Ghanmi, Abdeljabbar, Toumi, Faten (2011)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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A decomposition theorem for solutions of parabolic equations.

Watson, N.A. (2000)

Annales Academiae Scientiarum Fennicae. Mathematica

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Displaying similar documents to “Blow-up and global existence profile of a class of fully nonlinear degenerate parabolic equations”

A remark on the uniqueness of fundamental solutions to the p -Laplacian equation, p > 2 .

Hardy inequalities and dynamic instability of singular Yamabe metrics

Large time behavior of solutions to a class of doubly nonlinear parabolic equations

Regularity and uniqueness in quasilinear parabolic systems

A note on the Cahn-Hilliard equation in H 1 ( ℝ N ) involving critical exponent

Existence and asymptotic behaviour of positive solutions for some nonlinear parabolic systems in the half-space.

A decomposition theorem for solutions of parabolic equations.

A remark on the uniqueness of fundamental solutions to the $p$ -Laplacian equation, $p > 2$ .

A note on the Cahn-Hilliard equation in $H^{1} (ℝ^{N})$ involving critical exponent