Global in time solvability of the initial boundary value problem for some nonlinear dissipative evolution equations. (English) Zbl 0805.35077
Summary: The global in time solvability of the one-dimensional nonlinear equations of thermoelasticity, equations of viscoelasticity and nonlinear wave equations in several space dimensions with some boundary dissipation is discussed. The blow up of the solutions which might be possible even for small data is excluded by allowing for a certain dissipative mechanism.
MSC:
| 35L70 | Second-order nonlinear hyperbolic equations |
| 74A15 | Thermodynamics in solid mechanics |
| 35L20 | Initial-boundary value problems for second-order hyperbolic equations |
| 74D99 | Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) |
