On the existence and nonexistence of global solutions for the porous medium equation with strongly nonlinear sources in a cone

DOI10.1007/s00013-009-0081-9zbMath1194.35009OpenAlexW2019185397MaRDI QIDQ2380752

Chein-Shan Liu, Song Zhe Lian

Publication date: 12 April 2010

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00013-009-0081-9

zbMATH Keywords

existenceconeporous medium equationglobal nonnegative solutions

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Critical exponents in context of PDEs (35B33) Degenerate parabolic equations (35K65) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Quasilinear parabolic equations (35K59)

Related Items (2)

The critical Fujita exponent for a diffusion equation with a potential term ⋮ Semilinear pseudo-parabolic equations on manifolds with conical singularities

Cites Work

• Existence and nonexistence of global solutions for \(u_ t = \Delta u + a(x)u^ p\) in \(\mathbb{R}^ d\)
• The value of the critical exponent for reaction-diffusion equations in cones
• Nonexistence of solutions for parabolic inequalities in unbounded cone-like domains via the test function method.
• A critical behavior for some semilinear parabolic equations involving sign changing solutions
• The role of critical exponents in blow-up theorems: The sequel
• Blow-up results for nonlinear parabolic equations on manifolds
• On the Existence and Nonexistence of Global Solutions of Reaction-Diffusion Equations in Sectorial Domains
• The Role of Critical Exponents in Blowup Theorems
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