Global existence and decay for a system of two singular one-dimensional nonlinear viscoelastic equations with general source terms

ABSTRACT

The paper studies a system of two singular one-dimensional nonlinear equations that arise in generalized viscoelasticity with long-term memory, with general source terms and nonlocal boundary condition. We prove the existence of a global solution to the problem using the potential-well theory. Furthermore, we construct a Lyapunov functional and use it together with the perturbed energy method to prove a general decay result.

Keywords:

• Viscoelastic equations
• global existence
• general decay
• Lyapunov functional

2000 Mathematics Subject Classifications:

• 35L35
• 35L20

Acknowledgments

The authors would like to thank the anonymous referees and the handling editor for their careful reading and for relevant remarks/suggestions which helped them to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.