Global existence and blow-up of solutions to porous medium equation and pseudo-parabolic equation, I. Stratified Groups

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 [38] for stratified groups.

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Cited by in corpus (3)

• Compact Embeddings, Eigenvalue Problems, and subelliptic Brezis-Nirenberg equations involving singularity on stratified Lie groups
• Fujita-type results for the degenerate parabolic equations on the Heisenberg groups
• Blow-up solutions of damped Klein-Gordon equation on the Heisenberg group