On a class of quasilinear partial integrodifferential equations with singular kernels. (English) Zbl 0593.45011
The authors prove local and global existence theorems for the solution of an equation arising in nonlinear viscoelasticity, in which the memory function has a singularity. An approximation process by means of equations with regular kernels is indicated and the convergence of the approximate solution is proved by means of energy estimates.
Reviewer: C.Constanda
MSC:
| 45K05 | Integro-partial differential equations |
| 45L05 | Theoretical approximation of solutions to integral equations |
| 74D99 | Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) |
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