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Global existence, blow-up and asymptotic behavior of solutions for a class of p(x)-Choquard diffusion equations in RN

Boudjeriou, T ; Sharif University of Technology | 2022

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  1. Type of Document: Article
  2. DOI: 10.1016/j.jmaa.2021.125720
  3. Publisher: Academic Press Inc , 2022
  4. Abstract:
  5. In this paper, we investigate the local and global existence, asymptotic behavior, and blow-up of solutions to the Cauchy problem for Choquard-type equations involving the p(x)-Laplacian operator. As a particular case, we study the following initial value problem [Formula presented] where p,q,V:RN→R and α:RN×RN→R are continuous functions that satisfy some conditions which will be stated later on, and u0:RN→R is the initial function. Under some appropriate conditions, we prove the local and global existence of solutions for the above Cauchy problem by employing the abstract Galerkin approximation. Moreover, the blow-up of solutions and large-time behavior are also investigated. © 2021 Elsevier Inc
  6. Keywords:
  7. Blow-up ; Choquard diffusion equations ; Galerkin method ; Global existence ; p(x)-Laplacian
  8. Source: Journal of Mathematical Analysis and Applications ; Volume 506, Issue 2 , 2022 ; 0022247X (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0022247X2100799X