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Stabilizing asymptotic behaviour of a singularly perturbed hyperbolic equation. (Russian) Zbl 0762.35060
The author considers a semilinear hyperbolic equation with a small positive parameter multiplied by Laplace operator under periodic boundary conditions with respect to trivariate space variables. Sufficient existence conditions for stabilizing asymptotics are obtained.

MSC:
35L20 Initial-boundary value problems for second-order hyperbolic equations
35B25 Singular perturbations in context of PDEs
35L70 Second-order nonlinear hyperbolic equations
35B35 Stability in context of PDEs
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