Optimal results for parabolic problems arising in some physical models with critical growth in the gradient respect to a Hardy potential

DOI10.1016/j.aim.2010.04.028zbMath1213.35127OpenAlexW2038280029MaRDI QIDQ607336

Boumediene Abdellaoui, Ireneo Peral Alonso, A. R. M. Primo

Publication date: 22 November 2010

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2010.04.028

zbMATH Keywords

blow-upHardy potentialexistence and nonexistenceKardar-Parisi-Zhang equationquasi-linear parabolic equationsoptimal exponentFujita type exponent

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Critical exponents in context of PDEs (35B33) Initial value problems for second-order parabolic equations (35K15) Blow-up in context of PDEs (35B44) Hamilton-Jacobi equations (35F21) Quasilinear parabolic equations (35K59)

Related Items (7)

Strong regularizing effect of a gradient term in the heat equation with the Hardy potential ⋮ Effect of a Gradient Term on the Solvability of the Heat Equation with a Supercritical Reaction with Respect to the Hardy Potential ⋮ An approach without using Hardy inequality for the linear heat equation with singular potential ⋮ Strong regularizing effect of a gradient term in the heat equation with a weight ⋮ Qualitative properties of solutions to the Dirichlet problem for a Laplace equation involving the Hardy potential with possibly boundary singularity ⋮ Ireneo peral: forty years as mentor ⋮ On the heat equation with nonlinearity and singular anisotropic potential on the boundary

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