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Zeitschrift für Analysis und ihre Anwendungen


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Volume 33, Issue 1, 2014, pp. 21–41
DOI: 10.4171/ZAA/1497

Published online: 2013-12-27

Existence and Nonexistence of Global Solutions for Higher-Order Nonlinear Viscoelastic Equations

Yaojun Ye[1]

(1) Zhejiang University of Science and Technology, Hangzhou, China

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 $H_0^l(\Omega)$ and the decay of energy based on a difference inequality due to M.~Nakao is obtained. Meanwhile, under suitable conditions on relaxation function~$g(\cdot)$ 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.

Keywords: Nonlinear higher-order viscoelastic equation, initial-boundary value problem, global existence and nonexistence, decay estimate of solution

Ye Yaojun: Existence and Nonexistence of Global Solutions for Higher-Order Nonlinear Viscoelastic Equations. Z. Anal. Anwend. 33 (2014), 21-41. doi: 10.4171/ZAA/1497