Erhan Pişkin

Asymptotic behavior of a solution of the Cauchy problem for the generalized damped multidimensional Boussinesq equation

Abstract This work studies the Cauchy problem for the generalized damped multidimensional Boussinesq equation. By using a multiplier method, it is proven that the global solution of the problem decays to zero exponentially as the time approaches infinity, under a very simple and mild assumption regarding the nonlinear term.

Exponential decay and blow up of a solution for a system of nonlinear higher-order wave equations

This work studies a initial-boundary value problem of the weak damped nonlinear higher-order wave equations. Under suitable conditions on the initial datum, we prove that the solution decays exponentially and blows up with negative initial energy.

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

Abstract 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.

Blow up of a solution for a system of nonlinear higher-orderwave equations with strong damping terms

This work studies a initial-boundary value problem of the strong damped nonlinear higher-order wave equations. Under suitable conditions on the initial datum, we prove the blow up of the solution.

Growth of Solutions with Positive Initial Energy to Systems of Nonlinear Wave Equations with Damping and Source Terms

We consider initial-boundary conditions for coupled nonlinear wave equations with damping and source terms. We prove that the solutions of the problem are unbounded when the initial data are large enough in some sense.

Blow up of positive initial-energy solutions for a coupled nonlinear higher-order hyperbolic equations

This work studies an initial-boundary value problem of the coupled nonlinear higher-order hyperbolic equations with damping and source terms. Under suitable conditions on the initial datum, we prove the blow up of solutions with positive initial energy. We generalize some earlier results concerning the system.