Smoothing effects and infinite time blowup for reaction-diffusion equations: An approach via Sobolev and Poincare inequalities
Gabriele Grillo, Giulia Meglioli, Fabio Punzo
2021Virtual Community of Pathological Anatomy (University of Castilla La Mancha)12 citationsDOIOpen Access PDF
Abstract
We consider reaction-diffusion equations either posed on Riemannian manifolds or in the Euclidean weighted setting, with power-type nonlinearity and slow diffusion of porous medium type. We consider the particularly delicate case p
Topics & Concepts
MathematicsPointwiseSobolev inequalityType (biology)Sobolev spaceBounded functionPoincaré inequalityReaction–diffusion systemPure mathematicsCurvatureMathematical analysisSmoothingInequalityGeometryEcologyStatisticsBiologyAdvanced Mathematical Physics ProblemsNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in Engineering