A note on the global solutions of a degenerate parabolic system
type: Item
instance of: scholarly article
title: A note on the global solutions of a degenerate parabolic system
zbMATH Open document ID: 0884.35076
author: Qing Huang
author: K. Mochizuki
published in: Tokyo Journal of Mathematics
publication date: 1998-04-02T00:00:00Z
review text: The authors deal with the Cauchy problem of the degenerate parabolic system \[ \partial_t u=\Delta u^\alpha +v^p\;x\in\mathbb{R}^n,\;t>0, \quad \partial_t v=\Delta v^\beta +u^q \tag{*} \] with \(u(x,0)= u_0(x)\geq 0\), \(v(x,0)= v_0(x)\geq 0\). They establish the following theorem about the ``very fast diffusion'' case: \(0<\alpha\), \(\beta< (N-2)_+/N\), where \((M)_+ =\text{Max} \{M,0\}\). Theorem. When \(0<\alpha\), \(\beta< (N-2)_+/N\), \(p,q>1\), there exist nontrivial global solutions of the problem (*) for small initial functions.
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35K45
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 1054591
zbMATH Keywords: very fast diffusion
zbMATH Keywords: small initial functions
reviewed by: Akira Tsutsumi
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270042399
OpenAlex ID: W2051189386
DOI: 10.3836/TJM/1270042399
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description: scientific article; zbMATH DE number 1054591