On a Nonlinear Hyperbolic Volterra Equation
- 1 September 1980
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 11 (5) , 793-812
- https://doi.org/10.1137/0511071
Abstract
Summary:In this paper we consider a model of a one-dimensional body where strain depends on the history of stress. We show local existence for large data and global existence for small data of classical solutions and convergence of the displacement, strain and stress to zero for time going to infinityKeywords
This publication has 13 references indexed in Scilit:
- Frequency domain methods for Volterra equationsPublished by Elsevier ,2004
- Energy methods for nonlinear hyperbolic volterra integrodifferential equationsCommunications in Partial Differential Equations, 1979
- A forced quasilinear wave equation with dissipationPublished by Springer Nature ,1979
- A model for one-dimensional, nonlinear viscoelasticityQuarterly of Applied Mathematics, 1977
- An integro-differential equation with application in heat flowQuarterly of Applied Mathematics, 1977
- Global existence and asymptotics of the solutions of the second-order quasilinear hyperbolic equations with the first-order dissipationPublications of the Research Institute for Mathematical Sciences, 1977
- Positive definite measures with applications to a Volterra equationTransactions of the American Mathematical Society, 1976
- Variants of the Wiener-Levy Theorem, with Applications to Stability Problems for Some Volterra Integral EquationsAmerican Journal of Mathematics, 1975
- Existence and nonexistence in the large of solutions of quasilinear wave equationsArchive for Rational Mechanics and Analysis, 1967
- Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential EquationsJournal of Mathematical Physics, 1964