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On the nonlinear vibrations equation with a coefficient containing an integral. (English. Russian original) Zbl 0816.35089

Comput. Math. Math. Phys. 33, No. 9, 1171-1178 (1993); translation from Zh. Vychisl. Mat. Mat. Fiz. 33, No. 9, 1324-1332 (1993).
Summary: The existence and uniqueness of a global solution of a quasilinear hyperbolic equation in which there is a coefficient containing the integral of the gradient of the required function are proved. The coefficient is a non-negative and continuous function.

MSC:

35L70 Second-order nonlinear hyperbolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35L20 Initial-boundary value problems for second-order hyperbolic equations
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