Blow-up criteria for the semilinear parabolic equations driven by mixed local-nonlocal operators
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911219202392064 |
|---|---|
| author | Kumar, Vishvesh Torebek, Berikbol T. |
| author_facet | Kumar, Vishvesh Torebek, Berikbol T. |
| contents | The main goal of this paper is to establish \emph{necessary and sufficient conditions} for the nonexistence of a global solution to the semilinear heat equation with a mixed local--nonlocal operator $ -Δ+ (-Δ)^σ$, under a general time-dependent nonlinearity. Our results complement the recent work of Carhuas-Torre et al. [ArXiv, (2025), arXiv:2505.20401], in which the authors provide sufficient conditions for the existence and nonexistence of global solutions. In particular, our results recover the critical Fujita exponent for time-independent power-type nonlinearities, as obtained by Biagi et al. [Bull. London Math. Soc. (2024), 1--20] and Del Pezzo et al. [Nonlinear Anal. 255 (2025), 113761]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10014 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Blow-up criteria for the semilinear parabolic equations driven by mixed local-nonlocal operators Kumar, Vishvesh Torebek, Berikbol T. Analysis of PDEs 35K58, 35B33, 35A01, 35B44 The main goal of this paper is to establish \emph{necessary and sufficient conditions} for the nonexistence of a global solution to the semilinear heat equation with a mixed local--nonlocal operator $ -Δ+ (-Δ)^σ$, under a general time-dependent nonlinearity. Our results complement the recent work of Carhuas-Torre et al. [ArXiv, (2025), arXiv:2505.20401], in which the authors provide sufficient conditions for the existence and nonexistence of global solutions. In particular, our results recover the critical Fujita exponent for time-independent power-type nonlinearities, as obtained by Biagi et al. [Bull. London Math. Soc. (2024), 1--20] and Del Pezzo et al. [Nonlinear Anal. 255 (2025), 113761]. |
| title | Blow-up criteria for the semilinear parabolic equations driven by mixed local-nonlocal operators |
| topic | Analysis of PDEs 35K58, 35B33, 35A01, 35B44 |
| url | https://arxiv.org/abs/2509.10014 |