Work

Eternal solutions to a porous medium equation with strong nonhomogeneous absorption. Part II: Dead-core profiles

Year: 2025

Type: article

Abstract: Existence of a specific family of eternal solutions in exponential self-similar form is proved for the following porous medium equation with strong absorption: [Formula: see text] with [Formula: see text], [Formula: see text] and [Formula: see text]. Looking for solutions of the form [Formula: see text] it is shown that, for [Formula: see text], there exists a unique exponent [Formula: see text] for which there exists a one-parameter family of compactly supported profiles presenting a dead core. The precise behavior of the profiles at their interface is also determined. Moreover, the corresponding solutions show the optimal limitations for the finite time extinction property of genuine non-negative solutions to the Cauchy problem, studied in previous works.

Source: Analysis and Applications

DOI: 10.1142/s021953052550023x

Authors: Razvan Gabriel Iagar, Philippe Laurençot, Ariel Sánchez

Institutions: Universidad Rey Juan Carlos, Centre National de la Recherche Scientifique, Le LAMA, Université Savoie Mont Blanc

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Institut de Mathématiques de Toulouse, Universidad Rey Juan Carlos

OpenAlex ID: W4409151200

FWCI:

Cites: 30

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Related to: 10