Szczegóły publikacji
Opis bibliograficzny
Nonlocal Kirchhoff diffusion problems: local existence and blow-up of solutions / Xiang Mingqi, Vicenţiu D. RĂDULESCU, Binlin Zhang // Nonlinearity ; ISSN 0951-7715. — 2018 — vol. 31 no. 7, s. 3228–3250. — Bibliogr. s. 3249–3250, Abstr. — Publikacja dostępna online od: 2018-05-29. — V. Rădulescu - dod. afiliacja: University of Craiova, Romania
Autorzy (3)
- Mingqi Xiang
- AGHRǎdulescu Vicenţiu
- Zhang Binlin
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 117522 |
|---|---|
| Data dodania do BaDAP | 2018-10-26 |
| Tekst źródłowy | URL |
| DOI | 10.1088/1361-6544/aaba35 |
| Rok publikacji | 2018 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Nonlinearity |
Abstract
In this paper, we study a diffusion model of Kirchhoff-type driven by a nonlocal integro-differential operator. As a particular case, we consider the following diffusion problem {partial derivative(t)u + M ([u](s)(2) )(-Delta)s u = vertical bar u vertical bar(p-2)u in Omega x R+, partial derivative(t)u = partial derivative u/partial derivative t, u(x,t) = 0 in (R-N \ Omega) x R+, u(x, 0) = u(0)(x) in Omega, where [u](s) is the Gagliardo seminorm of u, Omega subset of R-N is a bounded domain with Lipschitz boundary, (-Delta)(s) isthe fractional-Laplacian with 0 < s < 1 < p < infinity, u(0) : Omega -> R+ is the initial function, and M : R-0(+)-> R-0(+) is continuous. Under some appropriate conditions, the local existence of nonnegative solutions is obtained by employing the Galerkin method. Then, by virtue of a differential inequality technique, we prove that the local nonnegative solutions blow-up in finite time with arbitrary negative initial energy and suitable initial values. Moreover, we give an estimate for the lower and upper bounds of the blow-up time. The main novelty is that our results cover the degenerate case, that is, the coefficient of (-Delta)(s) could be zero at the origin.
