Radial equivalence for the two basic nonlinear degenerate diffusion equations

By Razvan Gabriel Iagar, Ariel Sánchez, Juan Luis V'azquez. 2008

48 citations recorded by the source corpus.

Abstract In this paper we prove that there exists an explicit correspondence between the radially symmetric solutions of two well-known models of nonlinear diffusion, the porous medium equation and the p -Laplacian equation. We establish exact correspondence formulas between these solutions. We also study in detail the application of the results in the important case of self-similar solutions. In particular, we derive the existence of new self-similar solutions for the evolution p -Laplacian equation.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/8dc562e409da7dcb51fa26f13a42df887035e8b9

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

The Dirichlet Problem for the fractional p-Laplacian evolution equation (2015, background): “The close parallel that has been found between the theories of the standard Porous Medium Equation and the p-Laplacian equation, accredited in publications like [31, 54, 34], and the progress achieved in the study of fractional porous medium models makes it natural to investigate the fractional p-La”
Local smoothing effects, positivity, and Harnack inequalities for the fast p-Laplacian equation (2009, methodology): “This similarity is made explicit by the transformation described in [24] that establishes complete equivalence of the classes of radially symmetric solutions of both families of equations (note that the transformation maps m into p = m + 1 and may change the space dimension).”
Total Variation Flow and Sign Fast Diffusion in one dimension (2011, unknown): “[20].”
The Fisher–KPP problem with doubly nonlinear “fast” diffusion (2016, background): “A more complete analysis of the self-similarity of the p-Laplacian Equation can be found in [37].”