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A critical exponent in a degenerate parabolic equation
Author(s) -
Winkler Michael
Publication year - 2002
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.319
Subject(s) - exponent , degenerate energy levels , mathematics , critical exponent , cauchy distribution , mathematical physics , cauchy problem , combinatorics , mathematical analysis , initial value problem , physics , geometry , scaling , quantum mechanics , philosophy , linguistics
We consider positive solutions of the Cauchy problem in \documentclass{article}\usepackage{amsfonts}\begin{document}\pagestyle{empty}$\mathbb{R\,}^n$\end{document} for the equation $$u_t=u^p\,\Delta u+u^q,\quad p\geq1,\; q\geq 1$$\nopagenumbers\end and show that concerning global solvability, the number q = p + 1 appears as a critical growth exponent. Copyright © 2002 John Wiley & Sons, Ltd.