Self-similar solutions satisfying or not the equation of the interface.

DOI10.1016/S0022-247X(02)00450-XzbMath1106.35313OpenAlexW1983910790MaRDI QIDQ1857011

Ariel Sánchez, Arturo de Pablo

Publication date: 11 February 2003

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

Full work available at URL: https://doi.org/10.1016/s0022-247x(02)00450-x

zbMATH Keywords

Porous medium equationSelf-similar solutionsEquation of the interface

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Growth and boundedness of solutions to ordinary differential equations (34C11) Solutions to PDEs in closed form (35C05)

Related Items

Self-similar blow-up profiles for a reaction-diffusion equation with strong weighted reaction, Self-similar blow-up patterns for a reaction-diffusion equation with weighted reaction in general dimension, Blow-up and global existence for solutions to the porous medium equation with reaction and fast decaying density, Blow up profiles for a quasilinear reaction-diffusion equation with weighted reaction with linear growth

Cites Work

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• A quasilinar heat equation with a source: Peaking, localization, symmetry exact solutions, asymptotics, structures
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Thermal waves in absorbing media
• Existence and uniqueness on the very singular solution of the porous media equation with absorption
• On a class of similarity solutions of the porous media equation. III
• Applications of centre manifold theory
• Travelling waves and finite propagation in a reaction-diffusion equation
• On a class of similarity solutions of the porous media equation
• On a class of similarity solutions of the porous media equation. II
• Asymptotic behaviour and source-type solutions for a diffusion-convection equation
• Global travelling waves in reaction-convection-diffusion equations
• Regularity of interfaces in diffusion processes under the influence of strong absorption
• A very singular solution of the porous media equation with absorption
• Blow-up in quasilinear parabolic equations. Transl. from the Russian by Michael Grinfeld
• The characterization of reaction-convection-diffusion processes by travelling waves
• Nonuniqueness in nonlinear heat propagation: A heat wave coming from infinity
• Regularity properties of flows through porous media: The interface
• The Balance Between Strong Reaction And Slow Diffusion
• Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations
• The Porous Medium Equation in One Dimension
• Large-time behaviour of solutions of a reaction–diffusion equation
• SECOND-ORDER INTERFACE EQUATIONS FOR NONLINEAR DIFFUSION WITH VERY STRONG ABSORPTION
• Similarity solutions of the porous medium equation with sign changes