一类双重退化抛物型不等式问题解的Liouville 型定理

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A Liouville-type Theorem for a Doubly Degenerate Parabolic Inequality

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Abstract:

This paper deals with the nonexistence of nontrivial nonnegative global solutions to a doubly degenerate parabolic inequality u_t ≥ div(|\nabla
u| ^β\nabla u ^m)+u ^p on the half space S=Rⁿ×(0, ∞), where the parameters m≥1, p>1, β≥0. By using a test function method, we establish a Liouville-type theorem tha the inequality has no nontrivial nonnegative solution on S if m+β< p <m+β+β+2/n.

Key words: Critical Fujita exponent, Liouville-type theorem, Doubly degenerate, Parabolic inequality, blow-up

CLC Number:

35B33

JIANG Chao-Xin, ZHENG Si-Ning. A Liouville-type Theorem for a Doubly Degenerate Parabolic Inequality[J].Acta mathematica scientia,Series A, 2010, 30(3): 639-643.

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