Displaying similar documents to “The Cauchy problem for the system of partial differential equations describing nonsimple thermoelasticity”

On the theory of thermoelasticity

Henryk Kołakowski, Jarosław Łazuka (2011)

Applicationes Mathematicae

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The aim of this paper is to prove some properties of the solution to the Cauchy problem for the system of partial differential equations describing thermoelasticity of nonsimple materials proposed by D. Iesan. Explicit formulas for the Fourier transform and some estimates in Sobolev spaces for the solution of the Cauchy problem are proved.

On the Cauchy problem for linear PDEs with retarded arguments at derivatives

Krzysztof A. Topolski (2015)

Annales Polonici Mathematici

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We present an existence theorem for the Cauchy problem related to linear partial differential-functional equations of an arbitrary order. The equations considered include the cases of retarded and deviated arguments at the derivatives of the unknown function. In the proof we use Tonelli's constructive method. We also give uniqueness criteria valid in a wide class of admissible functions. We present a set of examples to illustrate the theory.