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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 et unicité de la solution pour un système de deux E.D.P.

Lahcen Ghannam (1989)

Publicacions Matemàtiques

We give some results on the existence, uniqueness and regularity of a nonlinear evolution system. This system models the viscoelastic behaviour of unicellular marine alga Acetabularia mediterrania when the calcium concentration varies. We show (with the aid of a fixed-point theorem) that the system admits a unique local solution in time.

Existence for a Cauchy-Dirichlet problem for evolutional p-Laplacian systems

Masashi Misawa (2004)

Applicationes Mathematicae

We study the existence of a weak solution to a Cauchy-Dirichlet problem for evolutional p-Laplacian systems with constant coefficients and principal term only. The initial-boundary data is assumed to be a bounded weak solution of an evolutional p-Laplacian system with an L¹-function as external force. The key ingredient is the maximum principle for weak solutions.

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