Parabolic equations in Musielak- Orlicz spaces with discontinuous in time N-function

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:290

Article

Bulicek, Miroslav¹  Gwiazda, Piotr²  Skrzeczkowski, Jakub³ 

[1] Charles Univ Prague, Fac Math & Phys, Math Inst, Sokolovska 83, Prague 18675, Czech Republic

[2] Polish Acad Sci, Inst Math, Jana & Jedrzeja Sniadeckich 8, PL-00656 Warsaw, Poland

[3] Univ Warsaw, Fac Math Informat & Mech, Stefana Banacha 2, PL-02097 Warsaw, Poland

关键词: Parabolic equation;    Non-standard growth;    Discontinuous N-function;    Existence;    Uniqueness;   

DOI  :  10.1016/j.jde.2021.04.017

来源: Elsevier

【 摘 要 】

We consider a parabolic PDE with Dirichlet boundary condition and monotone operator A with non -standard growth controlled by an N-function depending on time and spatial variable. We do not assume continuity in time for the N-function. Using an additional regularization effect coming from the equation, we establish the existence of weak solutions and in the particular case of isotropic N-function, we also prove their uniqueness. This general result applies to equations studied in the literature like p(t, x)-Laplacian and double-phase problems. (c) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free