Existence for a Cauchy–Dirichlet problem for evolutional $p$-Laplacian systems

Volume 31 / 2004

Masashi Misawa Applicationes Mathematicae 31 (2004), 287-302 MSC: 35D10, 35B65, 35K65. DOI: 10.4064/am31-3-4

Abstract

We study the existence of a weak solution to a Cauchy–Dirichlet problem for evolutional $p$-Laplacian systems with constant coefficients and principal term only. The initial-boundary data is assumed to be a bounded weak solution of an evolutional $p$-Laplacian system with an $L^1$-function as external force. The key ingredient is the maximum principle for weak solutions.

Authors

  • Masashi MisawaDepartment of Mathematics
    Faculty of Science
    Kumamoto University
    2-39-1 Kurokami, Kumamoto-shi
    Kumamoto 860-8555, Japan
    e-mail

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