Existence of a Renormalized Solution of a Parabolic Problem in Anisotropic Sobolev–Orlicz Spaces

被引：0
|
作者：
Vorob’yov N.A. [1 ]
Mukminov F.K. [2 ,3 ]
机构：
[1] Mavlyutov Institute of Mechanics, Ufa Federal Research Center of the Russian Academy of Sciences, Ufa
[2] Institute of Mathematics with Computing Center, Ufa Federal Research Center of the Russian Academy of Sciences, Ufa
[3] Ufa State Aviation Technical University, Ufa
来源：
Journal of Mathematical Sciences | 2021年 / 258卷 / 1期
关键词：
35K20; 35K55; 35K65; anisotropic parabolic equation; existence of solutions; N-function; nonpower nonlinearity; renormalized solution;
D O I：
10.1007/s10958-021-05535-8
中图分类号：
学科分类号：
摘要：
We consider the first mixed problem for a certain class of anisotropic parabolic equations of the form (β(xu))t′−diva(txu∇u)−b(txu∇u)=u where μ is a measure and the coefficients contain nonpower nonlinearities in the cylindrical domain DT = (0, T)×Ω, where Ω ⊂ ℝn is a bounded domain. We prove the existence of a renormalized solution of the problem for gt = 0 and a function β(x, r), which increases with respect to r and satisfies the Carath´eodory condition. © 2021, Springer Science+Business Media, LLC, part of Springer Nature.
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页码：37 / 64
页数：27
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