Existence, decay and blow up of solutions for the extensible beam equation with nonlinear damping and source terms : Open Mathematics

摘要

We consider the existence, both locally and globally in time, the decay and the blow up of the solution forthe extensible beam equation with nonlinear damping and source terms. We prove the existence of the solution byBanach contraction mapping principle. The decay estimates of the solution are proved by using Nakao’s inequality.Moreover, under suitable conditions on the initial datum, we prove that the solution blow up in finite time.