On the existence of viscosity solutions for the parabolic differential-functional Cauchy problem

Autor:	Krzysztof A. Topolski
Rok vydání:	2010
Předmět:	Cauchy problem Nonlinear system Cauchy's convergence test Elliptic partial differential equation Cauchy momentum equation General Mathematics Bounded function Mathematical analysis Cauchy boundary condition Hyperbolic partial differential equation Mathematics
Zdroj:	Acta Mathematica Hungarica. 129:277-296
ISSN:	1588-2632 0236-5294
DOI:	10.1007/s10474-010-0029-3
Popis:	We consider the nonlinear Cauchy problem for second order differential-functional equations of parabolic type, and present two existence theorems: in the class of bounded and in the class of unbounded viscosity solutions. These are based on differential inequalities and on the contraction method. The functional dependence in the equation is of Hale type. Our results cover equations with retarded and deviated argument, and differential-integral problems.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::a28f6b1bed971783d30e56be6300bb61 https://doi.org/10.1007/s10474-010-0029-3 Zobrazit plný text záznamu Plný text ve formátu PDF