On the absence of local solutions of several evolutionary problems

DOI10.1134/S000143460909003XzbMath1181.35304MaRDI QIDQ1048574

Evgeny Galakhov

Publication date: 12 January 2010

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

Sobolev spaceweak solutionheat equationDirichlet boundary conditionCarathéodory functionexistence problemquasilinear evolutionary PDE

Mathematics Subject Classification ID

Partial differential inequalities and systems of partial differential inequalities (35R45) Partial functional-differential equations (35R10) Weak solutions to PDEs (35D30) Blow-up in context of PDEs (35B44) Semilinear parabolic equations (35K58)

Related Items (6)

Instantaneous blow-up for nonlinear Sobolev type equations with potentials on Riemannian manifolds ⋮ Instantaneous blow-up versus local solvability for one problem of propagation of nonlinear waves in semiconductors ⋮ On the absence of weak solutions of nonlinear nonnegative higher order parabolic inequalities with a nonlocal source ⋮ On an instantaneous blow-up of solutions of evolutionary problems on the half-line ⋮ Instantaneous blow-up versus local solubility of the Cauchy problem for a two-dimensional equation of a semiconductor with heating ⋮ On the critical exponent “instantaneous blow-up” versus “local solubility” in the Cauchy problem for a model equation of Sobolev type

Cites Work

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• Abstract parabolic problems with critical nonlinearities and applications to Navier-Stokes and heat equations
• Linear and nonlinear heat equations in \(L^q_\delta\) spaces and universal bounds for global solutions

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