Global solution to the Cauchy problem of nonlinear thermodiffusion in a solid body

Arkadiusz Szymaniec

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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.

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Marie Kopáčková (1989)

Commentationes Mathematicae Universitatis Carolinae

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Thomas C. Sideris (1995)

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On a nonlinear wave equation with damping.

L. A. Medeiros, M. Milla Miranda (1990)

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On blowup of a solution to a Sobolev-type equation with a nonlocal source.

Korpusov, M.O., Sveshnikov, A.G. (2005)

Sibirskij Matematicheskij Zhurnal

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On strong globbal solutions of nonlinear hyperbolic equations

P. Brenner (1988-1989)

Séminaire Équations aux dérivées partielles (Polytechnique)

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Regularity and decay of 3D incompressible MHD equations with nonlinear damping terms

Zhuan Ye (2015)

Colloquium Mathematicae

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We prove the existence and uniqueness of global strong solutions to the Cauchy problem for 3D incompressible MHD equations with nonlinear damping terms. Moreover, the preliminary L² decay for weak solutions is also established.

Blowup of solutions for evolution equations with nonlinear damping.

Wu, Shun-Tang, Tsai, Long-Yi (2006)

Applied Mathematics E-Notes [electronic only]

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On the Cauchy Problem in Nonlinear 3-d-Thermoelasticity.

Reinhard Racke (1990)

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The support shrinking properties for solutions of quasilinear parabolic equations with strong absorption terms

Stanislav Antontsev, Jesus Ildefonso Díaz, Serguei I. Shmarev (1995)

Annales de la Faculté des sciences de Toulouse : Mathématiques

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