The Non Linear Cauchy Problem Of Operator Differential Equations
Marija Skendžić (1970)
Publications de l'Institut Mathématique
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Marija Skendžić (1970)
Publications de l'Institut Mathématique
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P. Besala (1983)
Annales Polonici Mathematici
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Henryk Kołakowski, Jarosław Łazuka (2008)
Applicationes Mathematicae
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The aim of this paper is to derive a formula for the solution to the Cauchy problem for the linear system of partial differential equations describing nonsimple thermoelasticity. Some properties of the solution are also presented. It is a first step to study the nonlinear case.
Oleg Zubelevich (2004)
Open Mathematics
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We consider an abstract version of the Cauchy-Kowalewski Problem with the right hand side being free from the Lipschitz type conditions and prove the existence theorem.
Byszewski, L. (1993)
Journal of Applied Mathematics and Stochastic Analysis
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Raetz, Juerg (1983)
Publications de l'Institut Mathématique. Nouvelle Série
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Jan Persson (1976)
Publications mathématiques et informatique de Rennes
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J. Ligęza (1975)
Colloquium Mathematicae
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Luigi Paganoni, S. Paganoni Martegalli (1989)
Aequationes mathematicae
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Mozgawa, Witold (2009)
Beiträge zur Algebra und Geometrie
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Tadeusz Śliwa (1981)
Colloquium Mathematicae
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M. Stojanović (1974)
Matematički Vesnik
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Ashordia, M. (1997)
Memoirs on Differential Equations and Mathematical Physics
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T. Śliwa (1988)
Applicationes Mathematicae
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Kent, Darrell C. (1984)
International Journal of Mathematics and Mathematical Sciences
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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.