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Global solution of nonlinear degenerate systems of filtration type in several space variables

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Abstract

In this paper the following nonlinear degenerate parabolic systems

$$u_t = \Delta _x (grad\varphi (u)) + \alpha \cdot \nabla b(u) + f(x,t,u)$$

with Dirichlet boundary conditions are discussed, where u, gradφ(u), b and f are vector valued functions and x∈Ω⊂R N. Under some structure conditions on the terms of the systems, the results on existence and uniqueness of global solutions of the systems are established.

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Authors and Affiliations

  1. Dept. of Math., Putian College, 351100, Fujian

    Lu Guofu

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  1. Lu Guofu
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The project supported by the National Natural Science Foundation of China and the Fujian Province Natural Science Foundation of China.

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Guofu, L. Global solution of nonlinear degenerate systems of filtration type in several space variables. Appl. Math. Chin. Univ. 14, 30–44 (1999). https://doi.org/10.1007/s11766-999-0052-8

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  • DOI: https://doi.org/10.1007/s11766-999-0052-8

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