Szczegóły publikacji
Opis bibliograficzny
Global well-posedness for a class of semilinear hyperbolic equations with singular potentials on manifolds with conical singularities / Yongbing Luo, Runzhang Xu, Chao YANG // Calculus of Variations and Partial Differential Equations ; ISSN 0944-2669. — 2022 — vol. 61 iss. 6 art. no. 210, s. 1–47. — Bibliogr. s. 46–47, Abstr. — Publikacja dostępna online od: 2022-09-26. — C. Yang - dod. afiliacja: Harbin Engineering University, Harbin, People’s Republic of China
Autorzy (3)
- Luo Yongbing
- Xu Runzhang
- AGHYang Chao
Dane bibliometryczne
| ID BaDAP | 143230 |
|---|---|
| Data dodania do BaDAP | 2022-11-16 |
| Tekst źródłowy | URL |
| DOI | 10.1007/s00526-022-02316-2 |
| Rok publikacji | 2022 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Calculus of Variations and Partial Differential Equations |
Abstract
This paper is concerned with a class of semilinear hyperbolic equations with singular potentials on the manifolds with conical singularities, which was introduced to describe a field propagating on the spacetime of a true string. We prove the local existence and uniqueness of the solution by using the contraction mapping principle. In the spirit of variational principle and mountain pass theorem, a class of initial data are precisely divided into three different energy levels. The main ingredient of this paper is to conduct a comprehensive and systematic study on the dynamic behavior of the solution with three different energy levels. We introduce a family of potential wells to derive a threshold of the existence of global solutions and blow up in finite time of solution in both cases with sub-critical and critical initial energy. Moreover, two sets of sufficient conditions for initial data leading to blow up result are established at arbitrarily positive initial energy level.
