Research Communication | Open Access
Volume 2019 | Communication ID 54
Volume 2019 | Communication ID 54
| Energy decay for a weakly nonlinear damped porous system with a nonlinear delay |
Abdelaziz Soufyane, Tijani Apalara
Received |
Accepted |
Published |
Jan 13, 2019 |
Jan 31, 2019 |
Mar 01, 2019 |
Abstract: This paper considers a one-dimensional porous system damped with a weakly nonlinear feedback in the presence of a nonlinear delay. Under appropriate assumptions on the weight of the delay and without imposing any restrictive growth assumption on the damping term at the origin, we establish an energy decay rate, using a perturbed energy method and some properties of convex functions in case of the same speed of propagation in the two equations of the system. Furthermore, we prove a global existence result using the Faedo-Galerkin procedure.