利用拓扑度法研究一类非线性抛物型问题弱解的存在性

Gulf Journal of Mathematics Pub Date : 2023-01-12 DOI:10.56947/gjom.v14i1.1091

Mohamed El Ouaarabi, C. Allalou, Melliani Melliani

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引用次数: 2

摘要

在本文中,我们研究的存在“弱的解决方案”的一类非线性抛物问题类型∂u⁄∂t - divΑ(x, t,∇u) =Φ(x, t) + div B (x, t, u,∇u)。使用Berkovits和Mustonen的拓扑度理论,我们证明弱解的存在性问题,在考虑在太空Lp (0, t, W01, p(Ω)),在ΩRN有限域,N≥2,p≥2。

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Existence of a weak solutions to a class of nonlinear parabolic problems via topological degree method

In this paper, we study the existence of "weak solutions" for a class of nonlinear parabolic problems of the type ∂ u⁄∂ t - div Α (x, t, ∇ u) = Φ (x, t) + div B(x, t, u, ∇ u). Using Berkovits and Mustonen's topological degree theory, we demonstrate the existence of a weak solutions to the problems under consideration in the space Lp(0, T, W01, p(Ω)), where Ω is a bounded domain in RN, N ≥ 2 and p ≥ 2.

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Gulf Journal of Mathematics

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