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

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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.

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Ruzhansky, M., Sabitbek, B., & Torebek, B. (2023). Global existence and blow-up of solutions to porous medium equation and pseudo-parabolic equation, I. Stratified groups. Manuscripta Mathematica, 171(3–4), 377–395. https://doi.org/10.1007/s00229-022-01390-2

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