NON WELL POSEDNESS OF PARABOLIC EQUATIONS WITH SUPERCRITICAL NONLINEARITIES

DOI10.1142/S0219199704001495zbMath1203.35131OpenAlexW2094208241MaRDI QIDQ4675803

José M. Arrieta, Aníbal Rodgriguez-Bernal

Publication date: 6 May 2005

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219199704001495

zbMATH Keywords

nonlinear boundary conditionsnonlinear heat equationsnon-well-posednessCritical exponentsweighted spaces proper minimal solutions

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Initial-boundary value problems for second-order parabolic equations (35K20) Critical exponents in context of PDEs (35B33) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

Related Items (11)

Supersolutions for a class of semilinear heat equations ⋮ Dissipative mechanism of a semilinear higher order parabolic equation in \(\mathbb R^N\) ⋮ Quantitative description on initial trace for the solvability to heat equation with exponential boundary in unbounded domain ⋮ A note on well-posedness of semilinear reaction-diffusion problem with singular initial data ⋮ Critical and supercritical higher order parabolic problems in \(\mathbb R^N\) ⋮ Solvability of the Heat Equation with a Nonlinear Boundary Condition ⋮ Sharp Estimate of the Life Span of Solutions to the Heat Equation with a Nonlinear Boundary Condition ⋮ On the instantaneous blow-up of solutions of some quasilinear evolution problems ⋮ Existence of solutions to the slow diffusion equation with a nonlinear source ⋮ On the absence of local solutions of several evolutionary problems ⋮ Heat equation with a nonlinear boundary condition and uniformly local \(L^r\) spaces

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