Self-similar solutions of the porous medium equation in a half-space with a nonlinear boundary condition: existence and symmetry

DOI10.1016/j.jmaa.2004.04.031zbMath1113.35077OpenAlexW1985347991MaRDI QIDQ1877811

Juan Dávila, Julio D. Rossi

Publication date: 19 August 2004

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2004.04.031

zbMATH Keywords

Elliptic equationsSymmetryNonlinear boundary conditions

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Nonlinear boundary value problems for linear elliptic equations (35J65) Reaction-diffusion equations (35K57) Geometric theory, characteristics, transformations in context of PDEs (35A30) Solutions to PDEs in closed form (35C05)

Related Items (2)

The Liouville theorem of a torsion system and its application to symmetry group of a porous medium type equation on symmetric spaces ⋮ Symmetry of positive solutions of elliptic equations with mixed boundary conditions in a sub-spherical sector

Cites Work

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• Symmetry and related properties via the maximum principle
• On a blow-up set for the quasilinear heat equation \(u_ t=(u^ \sigma u_ x)_ x + u^{\sigma+1}\)
• Existence of positive solutions of a semilinear elliptic equation in \(\mathbb{R}_+^n\) with a nonlinear boundary condition
• Blowup in diffusion equations: A survey
• Symmetry results for reaction-diffusion equations
• The problem of blow-up in nonlinear parabolic equations
• Uniqueness and stability of regional blow-up in a porous-medium equation
• Blow-up in quasilinear parabolic equations. Transl. from the Russian by Michael Grinfeld
• On a semilinear elliptic problem in \(\mathbb{R}^ N\) with a non-Lipschitzian nonlinearity
• Dual variational methods in critical point theory and applications
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• Nondegeneracy of blowup for semilinear heat equations
• On the blow-up set for u_t=du^m+u^m, m>1
• Continuation of blowup solutions of nonlinear heat equations in several space dimensions
• Symmetry of the blow‐up set of a porous medium type equation
• Symmetry in an elliptic problem and the blow—up set of

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