Journal
STUDIES IN APPLIED MATHEMATICS
Volume 149, Issue 3, Pages 798-814Publisher
WILEY
DOI: 10.1111/sapm.12521
Keywords
blowup; global existence; Hartree-type nonlinearity; wave-Hartree equation
Categories
Funding
- Innovative Funds Plan of Henan University of Technology [2020ZKCJ09]
- Natural Science Foundation of Henan Providence [202300410109]
- National Natural Science Foundation of China [11801145]
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In this paper, a class of wave equations of Hartree type on a bounded smooth convex domain with Dirichlet boundary condition is considered. The local existence result is obtained by applying the standard semigroup theory. The condition of global existence of weak solutions is derived using potential well theory. Blowup results for solutions when the initial energy is nonnegative or negative are given with the help of potential well theory and convexity method.
In this paper, we consider a class of wave equations of Hartree type on a bounded smooth convex domain with Dirichlet boundary condition. By applying the standard semigroup theory, we get the local existence result. Using potential well theory, we derive the condition of global existence of weak solutions. With the help of potential well theory and convexity method, we give blowup results for solutions when the initial energy is nonnegative or negative.
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