Turkish Journal of Mathematics
Global existence, uniform decay, and exponential growth of solutions for a system of viscoelastic Petrovsky equations
In this paper, we study the initial-boundary value problem for a system of nonlinear viscoelastic Petrovsky equations. Introducing suitable perturbed energy functionals and using the potential well method we prove uniform decay of solution energy under some restrictions on the initial data and the relaxation functions. Moreover, we establish a growth result for certain solutions with positive initial energy.
Global existence, uniform decay, exponential growth, viscoelastic Petrovsky equation
TAHAMTANI, FARAMARZ and PEYRAVI, AMIR
"Global existence, uniform decay, and exponential growth of solutions for a system of viscoelastic Petrovsky equations,"
Turkish Journal of Mathematics: Vol. 38:
1, Article 9.
Available at: https://journals.tubitak.gov.tr/math/vol38/iss1/9