A critical exponent in a degenerate parabolic equation | Zendy

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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.

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