Doubly nonlinear equation involving p(x)-homogeneous operators: Local existence, uniqueness and global behaviour

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:487

Article

Arora, Rakesh¹  Giacomoni, Jacques¹  Warnault, Guillaume¹ 

[1] UMR E2S UPPA CNRS 5142, LMAP, Batiment IPRA,Ave Univ, F-64013 Pau, France

关键词: Doubly nonlinear equation;    Polytropic filtration equation;    Leray-Lions operator with variable exponent;    Stabilization;   

DOI  :  10.1016/j.jmaa.2020.124009

来源: Elsevier

【 摘 要 】

In this work, we investigate the qualitative properties as uniqueness, regularity and stabilization of the weak solution to the nonlinear parabolic problem involving general p(x)-homogeneous operators: {q/2q - 1 partial derivative(t)(u(2q-1)) - del.a(x, del u) = f(x, u) + h(t, x)u(q-1) in (0, T) X Omega; u > 0 in (0, T) X Omega; u = 0 on (0, T) X partial derivative Omega; u(0, .) = u(0) in Omega. Thanks to the Picone's identity obtained in [10], we prove new results about comparison principles which yield a priori estimates, positivity and uniqueness of weak solutions. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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