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Effective computation of restoring force vector in finite element method

Martin Balazovjech, Ladislav Halada (2007)

Kybernetika

We introduce a new way of computation of time dependent partial differential equations using hybrid method FEM in space and FDM in time domain and explicit computational scheme. The key idea is quick transformation of standard basis functions into new simple basis functions. This new way is used for better computational efficiency. We explain this way of computation on an example of elastodynamic equation using quadrilateral elements. However, the method can be used for more types of elements and...

Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation

Jong Yeoul Park, Sun Hye Park (2006)

Czechoslovak Mathematical Journal

We consider the damped semilinear viscoelastic wave equation u ' ' - Δ u + ∫ 0 t h ( t - τ ) div { a ∇ u ( τ ) } d τ + g ( u ' ) = 0 in Ω × ( 0 , ∞ ) with nonlocal boundary dissipation. The existence of global solutions is proved by means of the Faedo-Galerkin method and the uniform decay rate of the energy is obtained by following the perturbed energy method provided that the kernel of the memory decays exponentially.

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 Global Solutions to Supercritical Semilinear Wave Equations

Georgiev, V. (1996)

Serdica Mathematical Journal

∗The author was partially supported by Alexander von Humboldt Foundation and the Contract MM-516 with the Bulgarian Ministry of Education, Science and Thechnology.In this work we study the existence of global solution to the semilinear wave equation (1.1) (∂2t − ∆)u = F(u), where F(u) = O(|u|^λ) near |u| = 0 and λ > 1. Here and below ∆ denotes the Laplace operator on R^n. The existence of solutions with small initial data, for the case of space dimensions n = 3 was studied by F. John in [13],...

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