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

Erhan Pişkin (2015)

Open Mathematics

We consider the existence, both locally and globally in time, the decay and the blow up of the solution for the extensible beam equation with nonlinear damping and source terms. We prove the existence of the solution by Banach 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.

Existence of a solution for a nonlinearly elastic plane membrane “under tension”

Daniel Coutand (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

A justification of the two-dimensional nonlinear “membrane” equations for a plate made of a Saint Venant-Kirchhoff material has been given by Fox et al. [9] by means of the method of formal asymptotic expansions applied to the three-dimensional equations of nonlinear elasticity. This model, which retains the material-frame indifference of the original three dimensional problem in the sense that its energy density is invariant under the rotations of 3 , is equivalent to finding the critical points...

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