摘要In this paper we consider a forth order nonlinear wave equation with dissi- pative boundary condition. We show that there are solutions under some conditions on initial data which blow up in finite time with positive initial energy.
1An L. J., Peirce A., A weakly nonlinear analysis of elasto-plastic-microstructure models. SIAM J. Appl. Math., 55 (1995), 136-155.
2Chen G., Yang Z., Existence and non-existence of global solutions for a class of nonlinear wave equations. Math. Methods Appl. Sci., 23 (2000), 615-631.
3Zhou Y., Global existence and nonexistence for a nonlinear wave equation with damping and source terms. Math. Nachr., 278 (2005), 1341-1358.
4Zhou Y., A blow-up result for a nonlinear wave equation with damping and vanishing initial energy in RN. Appl. Math. Lett., 18 (2005), 281-286.
5Zhou Y., Global nonexistence for a quasilinear evolution equation with critical lower energy. Arch. Inequal. Appl., 2 (2004), 41-47.
6Bilgin B. A., Kalantarov V. K., Blow up of solutions to the initial boundary value problem for quasilinear strongly damped wave equations. J. Math. Anal. Appl., 403 (2013), 89-94.
7Tahamtani F., Shahrouzi M., Existence and blow up of solutions to a Petrovsky equation with memory and nonlinear source term. Boundary Value Problems, 50 (2012), 1-15.
8Shahrouzi M., Tahamtani E, Global nonexistence and stability of the solutions of inverse problems for a class of Petrovsky systems. Georgian Math., J., 19 (2012), 575-586.
9Tahamtani F., Shahrouzi M., Asymptotic stability and blow up of solutions for a Petro- vsky inverse source problem with dissipative boundary condition. Math. Meth. Appl. Sci., 36 (2013), 829-839.
10Chen W., Zhou Y., Global nonexistence for a semilinear Petrovsky equation. Nonl. Anal., 70 (2009), 3203-3208.