Skip to main content

On a shock problem involving a nonlinear viscoelastic bar

Abstract

We treat an initial boundary value problem for a nonlinear wave equation in the domain,. The boundary condition at the boundary point of the domain for a solution involves a time convolution term of the boundary value of at, whereas the boundary condition at the other boundary point is of the form with and given nonnegative constants. We prove existence of a unique solution of such a problem in classical Sobolev spaces. The proof is based on a Galerkin-type approximation, various energy estimates, and compactness arguments. In the case of, the regularity of solutions is studied also. Finally, we obtain an asymptotic expansion of the solution of this problem up to order in two small parameters,.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Nguyen Thanh Long.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Long, N.T., Dinh, A.P.N. & Diem, T.N. On a shock problem involving a nonlinear viscoelastic bar. Bound Value Probl 2005, 718156 (2005). https://doi.org/10.1155/BVP.2005.337

Download citation