Non-existence of solutions for a non-Gaussian equation in fractional time with Osgood type nonlinearity
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929352146419712 |
|---|---|
| author | Solís, Soveny Vergara, Vicente |
| author_facet | Solís, Soveny Vergara, Vicente |
| contents | Osgood functions in the source term are used to produce results for non-existence of local solutions into the framework of non-Gaussian diffusion equations. The critical exponent for non-existence of local solutions is found to depend on the fractional derivative, the non-Gaussian diffusion and the non-linear term. The instantaneous blow-up phenomenon is studied by exploiting estimates of the fundamental solutions. Nevertheless, theory of super-solutions and fixed points are combined for showing existence of global solutions. In this case, the critical exponent for existence of global solutions depends only on the last two parameters above. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13151 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-existence of solutions for a non-Gaussian equation in fractional time with Osgood type nonlinearity Solís, Soveny Vergara, Vicente Analysis of PDEs Functional Analysis AMS subject classification: 35B44 (primary), 35C15, 35B33, 47A52 Osgood functions in the source term are used to produce results for non-existence of local solutions into the framework of non-Gaussian diffusion equations. The critical exponent for non-existence of local solutions is found to depend on the fractional derivative, the non-Gaussian diffusion and the non-linear term. The instantaneous blow-up phenomenon is studied by exploiting estimates of the fundamental solutions. Nevertheless, theory of super-solutions and fixed points are combined for showing existence of global solutions. In this case, the critical exponent for existence of global solutions depends only on the last two parameters above. |
| title | Non-existence of solutions for a non-Gaussian equation in fractional time with Osgood type nonlinearity |
| topic | Analysis of PDEs Functional Analysis AMS subject classification: 35B44 (primary), 35C15, 35B33, 47A52 |
| url | https://arxiv.org/abs/2405.13151 |