Mixed problem for systems of hyperbolic equations with nonlinear boundary dissipation and a nonlinear source of variable growth order. (English. Russian original) Zbl 1498.35353
Differ. Equ. 58, No. 8, 1028-1042 (2022); translation from Differ. Uravn. 58, No. 8, 1039-1052 (2022).
Summary: We study a mixed problem for systems of one-dimensional semilinear hyperbolic equations with variable nonlinearity growth rate and nonlinear boundary conditions. Theorems on the local solvability and blow-up of solutions in finite time are proved.
MSC:
| 35L50 | Initial-boundary value problems for first-order hyperbolic systems |
| 35L60 | First-order nonlinear hyperbolic equations |
| 35B44 | Blow-up in context of PDEs |
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