On a class of differential equations of parabolic type with impulsive action
type: Item
instance of: scholarly article
title: On a class of differential equations of parabolic type with impulsive action
zbMATH Open document ID: 1193.34122
DOI: 10.1134/S0012266108020110
author: A. D. Myshkis
author: L. A. Vlasenko
author: A. G. Rutkas
published in: Differential Equations
publication date: 2010-01-15T00:00:00Z
review text: For the class of semi-linear abstract differential equations with impulsive action of the form \[ \begin{gathered} \frac{d}{dt}\,[ Au(t)]+Bu(t)= f(t,u(t)),\quad t>t_0, \,\, t\notin\{t_k\},\\ \Delta u|_{t=t_{k}}=u(t_k+0)-u(t_k-0)=I_k(u(t_k-0)), \,\,\, k=1,2,\ldots, \end{gathered} \] the existence and uniqueness of solutions are studied. Here \(A,B\) are closed linear operators mapping a complex Banach space \(X\) into another complex Banach space \(Y,\) \(f: [t_0,\infty)\times X\to Y\) is a continuous function, \(I_k:\Omega_k\subset X\to X\) and \(t_0<t_1<t_2<\ldots.\) The abstract results are applied to partial differential equations with impulsive action.
reviewed by: Sotiris K. Ntouyas
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 35R12
Mathematics Subject Classification ID: 34A37
Mathematics Subject Classification ID: 34A09
zbMATH DE Number: 5659345
zbMATH Keywords: Impulsive partial differential equations
zbMATH Keywords: implicit equations
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
MaRDI profile type: Publication
cites work: Degenerate non-stationary differential equations with delay in Banach spaces.
cites work: Geometric theory of semilinear parabolic equations
full work available at URL: s0012266108020110
OpenAlex ID: W2038860263
description: scientific article; zbMATH DE number 5659345