Szczegóły publikacji
Opis bibliograficzny
Time-space fractional diffusion problems: existence, decay estimates and blow-up of solutions / Ruixin Shen, Mingqi Xiang, Vicenţiu D. RĂDULESCU // Milan Journal of Mathematics ; ISSN 1424-9286. — 2022 — vol. 90 iss. 1, s. 103–129. — Bibliogr. s. 126–128, Abstr. — Publikacja dostępna online od: 2022-03-22. — V. D. Rădulescu - dod. afiliacja: Department of Mathematics, China-Romania Research Center in Applied Mathematics, University of Craiova, Craiova, Romania
Autorzy (3)
- Shen Ruixin
- Xiang Mingqi
- AGHRǎdulescu Vicenţiu
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 141276 |
|---|---|
| Data dodania do BaDAP | 2022-07-29 |
| Tekst źródłowy | URL |
| DOI | 10.1007/s00032-021-00348-5 |
| Rok publikacji | 2022 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Creative Commons | |
| Czasopismo/seria | Milan Journal of Mathematics |
Abstract
The aim of this paper is to study the following time-space fractional diffusion problem {partial derivative(beta)(t)u + (-Delta)(alpha)u + (-Delta)(alpha) partial derivative(beta)(t)u = lambda f(x,u) + g(x,t) in Omega x R+, u(x,t) = 0 in (R-N\Omega) x R+, u(x,0) = u(0)(x) in Omega, where Omega subset of R-N is a bounded domain with Lipschitz boundary, (-Delta)(alpha) is the fractional Laplace operator with 0 < alpha < 1, partial derivative(beta)(t) is the Riemann-Liouville time fractional derivative with 0 < beta < 1, lambda is a positive parameter, f : Omega x R -> R is a continuous function, and g is an element of L-2(0,infinity; L-2(Omega)). Under natural assumptions, the global and local existence of solutions are obtained by applying the Galerkin method. Then, by virtue of a differential inequality technique, we give a decay estimate of solutions. Moreover, the blow-up property of solutions is also investigated.
