Blow‐up phenomena for a class of fourth‐order nonlinear wave equations with a viscous damping term

Abstract

Communicated by M. GrovesThis paper deals with the blow-up phenomena for a class of fourth-order nonlinear wave equations with a viscous damping term

Initial and Boundary Value Problems for a Class of Nonlinear Metaparabolic Equations

“…Equation 1is also closely connected with many equations [26][27][28][29]. For example, Yang [26] considered the initial and boundary value problems of the following equation…”

“…Furthermore, Xu et al [28] considered the initial and boundary value problems and proved the global existence and nonexistence of solutions by adopting and modifying the so called concavity method under some conditions with low initial energy. Ali Khelghati and Khadijeh Baghaei [29] proved that the blow up for Equation (12) occurs in finite time for arbitrary positive initial energy.…”

On decay and blow-up of solutions for a nonlinear beam equation with double damping terms

“…Furthermore, Aassila and Guesmia in [9] solved the energy decay problem for ⊂ R m . Later on, their results were extended to various problems, for more investigations and different points of view we refer to [10][11][12][13][14][15][16][17][18][19][20][21] and the references therein.…”

“…We construct a differential inequality under certain conditions. The method applied is the so-called "concavity method" [21]. As an application of the above results, one example of nonexistence of a global solution is given.…”