Convergence estimates for abstract second order differential equations with two small parameters and Lipschitzian nonlinearities
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Published:2021-11-15
Issue:1
Volume:38
Page:179-200
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ISSN:1584-2851
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Container-title:Carpathian Journal of Mathematics
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language:
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Short-container-title:CJM
Author:
PERJAN ANDREI, ,RUSU GALINA,
Abstract
In a real Hilbert space $H$ we consider the following singularly perturbed Cauchy problem ... We study the behavior of solutions $u_{\varepsilon\delta}$ in two different cases: $\varepsilon\to 0$ and $\delta \geq \delta_0>0;$ $\varepsilon\to 0$ and $\delta \to 0,$ relative to solution to the corresponding unperturbed problem.We obtain some {\it a priori} estimates of solutions to the perturbed problem, which are uniform with respect to parameters, and a relationship between solutions to both problems. We establish that the solution to the unperturbed problem has a singular behavior, relative to the parameters, in the neighbourhood of $t=0.$
Publisher
Technical University of Cluj Napoca, North University Center of Baia Mare
Subject
General Mathematics