A class of evolution equations: Existence of solutions with functional boundary conditions
type: Item
instance of: scholarly article
title: A class of evolution equations: Existence of solutions with functional boundary conditions
zbMATH Open document ID: 0942.34052
DOI: 10.1007/BF02675008
published in: Mathematical Notes
publication date: 2000-08-21T00:00:00Z
review text: The evolution equation \[ \dot u(t)= Au(t)+ g(u)(t),\quad 0\leq t\leq 1, \] is considered with \(u\) taking values in a Banach space \(X\). Here, \(A\) is a linear (possibly unbounded) operator on \(X\) generating a strongly continuous semigroup, and \(g\) is a continuous map in functional spaces. The existence of a solution \(u\) is proved that satisfies for all \(t\) the phase restriction \(u(t)\in K\), with \(K\subset X\) being a fixed closed convex set, and the boundary condition \(u(0)= \varphi(u)\), with \(\varphi\) defined on a functional space and taking values in \(X\). In particular, initial and periodic conditions can be considered.
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 47H30
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 1407533
zbMATH Keywords: evolution equation
zbMATH Keywords: nonlinear boundary value problem
zbMATH Keywords: phase restriction
zbMATH Keywords: existence of solutions
author: Vladimir V. Goncharov
author: S. A. Timoshin
reviewed by: Sergei A. Brykalov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1407533