Displaying similar documents to “Global solution to the Cauchy problem of nonlinear thermodiffusion in a solid body”

Initial-boundary value problem in nonlinear hyperbolic thermoelasticity. Some applications in continuum mechanics

Jerzy August Gawinecki

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The aim of this paper is to present an elementary self-contained introduction to some important aspects of the theory of local (in time) solutions to the initial-boundary value problem for nonlinear hyperbolic equations of thermoelasticity theory. The relevant existence theorem is proved using the approach of Kato via semigroup theory for the associated linearized problem. Next, we prove an energy estimate in a suitably chosen Sobolev space for the solution of the linearized problem,...

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

Erhan Pişkin (2015)

Open Mathematics

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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.