The initial-boundary value problem for some nonlinear higher-order viscoelastic equation with damping and source terms in a bounded domain is studied. The existence of global solutions for this problem is established by constructing a stable set in and the decay of energy based on a difference inequality due to M.
Nakao is obtained. Meanwhile, under suitable conditions on relaxation function and the positive initial energy, it is proved that the solution blows up in the finite time and the lifespan estimates of solutions are also given.
Cite this article
Yaojun Ye, Existence and Nonexistence of Global Solutions for Higher-Order Nonlinear Viscoelastic Equations. Z. Anal. Anwend. 33 (2014), no. 1, pp. 21–41DOI 10.4171/ZAA/1497