On the global solvability of porous media equations with general (spatially dependent) advection terms
N. M. L. Diehl (Instituto Federal de Educa\c{c}\~ao, Ci\^encia e, Tecnologia), L. Fabris (Universidade Federal de Santa Maria), P. R., Zingano (Universidade Federal do Rio Grande do Sul)
TL;DR
This paper proves that certain advection-diffusion equations with porous media diffusion and integrable initial data are globally solvable under mild conditions, expanding understanding of their long-term behavior.
Contribution
It establishes global solvability results for porous media equations with spatially dependent advection, including generalizations and related findings.
Findings
Global solvability under mild conditions
Applicability to equations with spatially dependent advection
Extensions to related models
Abstract
We show that advection-diffusion equations with porous media type diffusion and integrable initial data are globally solvable under very mild conditions. Some generalizations and related results are also given.
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Taxonomy
TopicsDifferential Equations and Numerical Methods · Nonlinear Partial Differential Equations · Nonlinear Differential Equations Analysis