Blow-up of solution for an integro-differential equation with arbitrary positive initial energy
作者： Liu Jie , Liang Fei
DOI: 10.1186/S13661-015-0361-1
关键词: Partial differential equation 、 Ordinary differential equation 、 Omega 、 Dirichlet boundary condition 、 Energy (signal processing) 、 Integro-differential equation 、 Mathematics 、 Nabla symbol 、 Mathematical analysis
摘要: In this paper, we consider the integro-differential equation $u_{tt}-M(\|\nabla u\|^{2}_{2})\Delta u+ \int_{0}^{t} g(t-\tau)\Delta u(\tau)\, d\tau+ u_{t}=f(u)$ , $(x,t)\in\Omega\times(0,T)$ with initial and Dirichlet boundary conditions. Under suitable assumptions on functions g data, a blow-up result arbitrary positive energy is established.
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