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Finite-dimensional approximation of solutions for a nonlinear system of coupled hyperbolic equations. (Chinese. English summary) Zbl 0968.35012
The paper concerns the system of two nonlinear wave equations \left.\begin{aligned} u_{tt} &-D_1\Delta u-p_1 u+p_2 uv= f(x,t)\\ v_{tt} &-D_2\Delta v- p_2 uv+ p_3v= g(x,t)\end{aligned}\right\} x\in\Omega,\;t>0 with homogeneous Dirichlet boundary conditions and initial conditions $$u|_{t=0}= \varphi_1$$, $$v|_{t=0}= \psi_1$$, $$u_t|_{t=0}= \psi_2$$, $$v_t|_{t=0}= \psi_2$$. The approximating solutions are constructed by means of the eigenfunctions of the eigenvalue problem $$-\Delta w= \lambda w$$ in $$\Omega$$, $$u= 0$$ on $$\partial\Omega$$.
##### MSC:
 35A35 Theoretical approximation in context of PDEs 35L70 Second-order nonlinear hyperbolic equations 35L55 Higher-order hyperbolic systems