Nonexistence of global solutions of a class of coupled nonlinear Klein-Gordon equations with nonnegative potentials and arbitrary initial energy
| dc.creator | Wang, Yanjin | |
| dc.date | 2007-02-06 | |
| dc.date.accessioned | 2026-07-07T07:45:04Z | |
| dc.date.available | 2026-07-07T07:45:04Z | |
| dc.description | In the paper we consider the nonexistence of global solutions of the Cauchy problem for coupled Klein-Gordon equations of the form \begin{eqnarray*} \left\{\begin{array}{l} u_{tt}-Δu+m_1^2 u+K_1(x)u=a_1|v|^{q+1}|u|^{p-1}u v_{tt}-Δv+m_2^2 u+K_2(x)v=a_2|u|^{p+1}|v|^{q-1}v u(0,x)=u_0; u_t(0,x)=u_1(x) v(0,x)=v_0; v_t(0,x)=v_1(x) \end{array} \right. \end{eqnarray*} on $\R\times\R^n$. Firstly for some special cases of $n=2,3$, we prove the existence of ground state of the corresponding Lagrange-Euler equations of the above equations. Then we establish a blow up result with low initial energy, which leads to instability of standing waves of the system above. Moreover as a byproduct we also discuss the global existence. Next based on concavity method we prove the blow up result for the system with non-positive initial energy in the general case: $n\geq 1$. Finally when the initial energy is given arbitrarily positive, we show that if the initial datum satisfies some conditions, the corresponding solution blows up in a finite time. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/math/0702132 | |
| dc.identifier | http://arxiv.org/abs/math/0702132 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123418 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 34A34, 35G25, 35L70, 35J60 | |
| dc.title | Nonexistence of global solutions of a class of coupled nonlinear Klein-Gordon equations with nonnegative potentials and arbitrary initial energy | |
| dc.type | text |