Global existence for parabolic problems involving the $p$-Laplacian and a critical gradient term

DOI10.1512/iumj.2009.58.3409zbMath1171.35011OpenAlexW2042833397MaRDI QIDQ3627571

Daniela Giachetti, Sergio Segura de León, Andrea Dall'Aglio

Publication date: 13 May 2009

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1512/iumj.2009.58.3409

zbMATH Keywords

a priori estimatesconvection-diffusion problemslogarithmic Sobolev inequalitiesnonlinear parabolic problemsexistence and regularitybounded and unbounded solutionsgradient term with natural growth

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Reaction-diffusion equations (35K57) Initial-boundary value problems for second-order parabolic equations (35K20) Critical exponents in context of PDEs (35B33) Degenerate parabolic equations (35K65) A priori estimates in context of PDEs (35B45)

Related Items (10)

On the solvability of the Dirichlet problem for anisotropic parabolic equations in non-convex domains ⋮ Quasilinear equations with degenerate coerciveness and having multiple singularities ⋮ Existence results for a Cauchy-Dirichlet parabolic problem with a repulsive gradient term ⋮ Asymptotic behavior of solutions for nonlinear parabolic operators with natural growth term and measure data ⋮ On the existence of radially symmetric solutions for the \(p \)-Laplace equation with strong gradient nonlinearities ⋮ Influence of Gradient Terms on the Existence of Solutions to the Dirichlet Problem for p-Laplacian ⋮ On some parabolic equations involving superlinear singular gradient terms ⋮ Radially Symmetric Solutions of the p-Laplace Equation with Gradient Terms ⋮ Existence result to a parabolic equation with quadratic gradient term and an \(L^1\) source ⋮ Some results on a singular parabolic equation in one dimension case

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