An abstract non-linear Cauchy-Kowalewski theorem and its proof by a contraction-mapping principle
W. Tutschke (1986)
Matematički Vesnik
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W. Tutschke (1986)
Matematički Vesnik
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Byszewski, L. (1993)
Journal of Applied Mathematics and Stochastic Analysis
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Tomás Domínguez Benavides (1980)
Collectanea Mathematica
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Byszewski, L. (1992)
Journal of Applied Mathematics and Stochastic Analysis
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Łukasz Dawidowski (2015)
Annales Mathematicae Silesianae
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The abstract Cauchy problem on scales of Banach space was considered by many authors. The goal of this paper is to show that the choice of the space on scale is significant. We prove a theorem that the selection of the spaces in which the Cauchy problem ut − Δu = u|u|s with initial–boundary conditions is considered has an influence on the selection of index s. For the Cauchy problem connected with the heat equation we will study how the change of the base space influents the regularity...
Raetz, Juerg (1983)
Publications de l'Institut Mathématique. Nouvelle Série
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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.
Yu G. Rykov (1993)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
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Iryna Banakh, Taras Banakh, Anatolij Plichko, Anatoliy Prykarpatsky (2012)
Open Mathematics
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We find conditions for a smooth nonlinear map f: U → V between open subsets of Hilbert or Banach spaces to be locally convex in the sense that for some c and each positive ɛ < c the image f(B ɛ(x)) of each ɛ-ball B ɛ(x) ⊂ U is convex. We give a lower bound on c via the second order Lipschitz constant Lip2(f), the Lipschitz-open constant Lipo(f) of f, and the 2-convexity number conv2(X) of the Banach space X.
Sova, M.
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Marija Skendžić (1970)
Publications de l'Institut Mathématique
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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.
Ćirić, Ljubomir B. (1990)
Publications de l'Institut Mathématique. Nouvelle Série
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