Bounded solutions of nonlinear hyperbolic equations with time delay
Date
2018-01-15
Authors
Ashyralyev, Allaberen
Agirseven, Deniz
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We consider the initial value problem
d2u/dt2 + Au(t) = ƒ(u(t), u(t - w)), t > 0,
u(t) = ϕ(t), -w ≤ t ≤ 0
for a nonlinear hyperbolic equation with time delay in a Hilbert space with the self adjoint positive definite operator A. We establish the existence and uniqueness of a bounded solution, and show application of the main theorem for four nonlinear partial differential equations with time delay. We present first and second order accuracy difference schemes for the solution of one dimensional nonlinear hyperbolic equation with time delay. Numerical results are also given.
Description
Keywords
Nonlinear hyperbolic equation, Time delay, Bounded solution
Citation
Ashyralyev, A., & Agirseven, D. (2018). Bounded solutions of nonlinear hyperbolic equations with time delay. <i>Electronic Journal of Differential Equations, 2018</i>(21), pp. 1-15.
Rights
Attribution 4.0 International