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Mixed problem with dynamical transmission condition for a one-dimensional hyperbolic equation with strong dissipation. (English) Zbl 1471.35195

Summary: In this paper, we study a mixed problem for the nonlinear hyperbolic equation with a strong dissipation and a dynamical transmission condition. The existence and uniqueness theorems of local and global solutions are proved.

MSC:

35L53 Initial-boundary value problems for second-order hyperbolic systems
35L71 Second-order semilinear hyperbolic equations
35B40 Asymptotic behavior of solutions to PDEs
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