The heat equation with singular nonlinearity and singular initial data

DOI10.1016/j.jde.2006.07.007zbMath1106.35026OpenAlexW2004043670MaRDI QIDQ852687

Miguel Loayza

Publication date: 15 November 2006

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2006.07.007

zbMATH Keywords

existenceuniquenesspositive solutionsconcave-convex nonlinearity

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Analyticity in context of PDEs (35A20)

Related Items (8)

Stability of stationary solutions for semilinear heat equations with concave nonlinearity ⋮ Random attractors for stochastic parabolic equations with additive noise in weighted spaces ⋮ Stability and instability of stationary solutions for sublinear parabolic equations ⋮ Dynamics of non-autonomous parabolic problems with subcritical and critical nonlinearities ⋮ A necessary and sufficient condition for uniqueness of the trivial solution in semilinear parabolic equations ⋮ Non-autonomous parabolic problems with singular initial data in weighted spaces ⋮ Attractors for non-autonomous parabolic problems with singular initial data ⋮ On the local existence for a weakly parabolic system in Lebesgue spaces

Cites Work

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• A nonlinear heat equation with singular initial data
• Non-unicité des solutions d'une équation d'évolution non-linéaire
• NON-UNIQUENESS FOR A CRITICAL NON-LINEAR HEAT EQUATION
• Global existence, asymptotic behavior and self-similar solutions for a class of semilinear parabolic systems

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