Global existence and blow-up of solutions to porous medium equation and pseudo-parabolic equation, I. Stratified groups
Michael Ruzhansky, Bolys Sabitbek, Berikbol T. Torebek
Abstract
Abstract In this paper, we prove a global existence and blow-up of the positive solutions to the initial-boundary value problem of the nonlinear porous medium equation and the nonlinear pseudo-parabolic equation on the stratified Lie groups. Our proof is based on the concavity argument and the Poincaré inequality, established in Ruzhansky and Suragan (J Differ Eq 262:1799–1821, 2017) for stratified groups.
Topics & Concepts
MathematicsMathematical analysisNonlinear systemPorous mediumParabolic partial differential equationPartial differential equationPorosityPhysicsGeotechnical engineeringEngineeringQuantum mechanicsNonlinear Partial Differential EquationsAdvanced Mathematical Physics ProblemsGeometric Analysis and Curvature Flows