Nonlinear diffusions and optimal constants in Sobolev type inequalities: Asymptotic behaviour of equations involving the \(p\)-Laplacian

DOI10.1016/S1631-073X(02)02225-2zbMath1090.35096OpenAlexW1990783209MaRDI QIDQ1600116

Jean Dolbeault, Manuel A. del Pino

Publication date: 2002

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s1631-073x(02)02225-2

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items

Global well-posedness for pseudo-parabolic p-Laplacian equation with singular potential and logarithmic nonlinearity, Asymptotic expansion of solutions to the Cauchy problem for doubly degenerate parabolic equations with measurable coefficients, Global existence and decay estimates of energy of solutions for a new class of \(p\)-Laplacian heat equations with logarithmic nonlinearity, The lifespan of solutions for a viscoelastic wave equation with a strong damping and logarithmic nonlinearity, The Cauchy problem for the fast \(p\)-Laplacian evolution equation. Characterization of the global Harnack principle and fine asymptotic behaviour, On the minimum \(f\)-divergence for given total variation, Blow up and decay for a class of \(p\)-Laplacian hyperbolic equation with logarithmic nonlinearity, Grow-up of weak solutions in a \(p\)-Laplacian pseudo-parabolic problem, Global solution and blow-up for a class of pseudo \(p\)-Laplacian evolution equations with logarithmic nonlinearity, Global solution and blow-up for a class of \(p\)-Laplacian evolution equations with logarithmic nonlinearity, Note on affine Gagliardo-Nirenberg inequalities, Functional inequalities and applications to doubly nonlinear diffusion equations, Large time asymptotics of the doubly nonlinear equation in the non-displacement convexity regime, Asymptotic behavior for doubly degenerate parabolic equations, Ground state solution for a fourth-order elliptic equation with logarithmic nonlinearity modeling epitaxial growth, Existence results for a class of the quasilinear elliptic equations with the logarithmic nonlinearity, Infinite time blow-up of solutions to a fourth-order nonlinear parabolic equation with logarithmic nonlinearity modeling epitaxial growth, Rates of decay to equilibria for \(p\)-Laplacian type equations, Global existence and blow-up for the fractional \(p\)-Laplacian with logarithmic nonlinearity, Unnamed Item, Global existence and blow-up for a parabolic problem of Kirchhoff type with logarithmic nonlinearity, Nonlinear diffusions, hypercontractivity and the optimal \(L^{p}\)-Euclidean logarithmic Sobolev inequality, Global existence and blow-up for a mixed pseudo-parabolic \(p\)-Laplacian type equation with logarithmic nonlinearity, A \(p\)-Laplace equation with logarithmic nonlinearity at high initial energy level, Global well-posedness of solutions for the \(p\)-Laplacian hyperbolic type equation with weak and strong damping terms and logarithmic nonlinearity, Nonlinear diffusions and optimal constants in Sobolev type inequalities: Asymptotic behaviour of equations involving the \(p\)-Laplacian

Cites Work

• Degenerate parabolic equations
• Fundamental solutions and asymptotic behaviour for the p-Laplacian equations
• Nonlinear diffusions and optimal constants in Sobolev type inequalities: Asymptotic behaviour of equations involving the \(p\)-Laplacian
• Uniqueness of ground states for quasilinear elliptic equations
• ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• The Asymptotic Behavior of Gas in an n-Dimensional Porous Medium
• Sur l'inégalité logarithmique de Sobolev
• Asymptotic L^1-decay of solutions of the porous medium equation to self-similarity
• Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities