Non-autonomous inhomogeneous boundary Cauchy problems

Non-autonomous inhomogeneous boundary Cauchy problems

In this paper we prove existence and uniqueness of classical solutions for the non-autonomous inhomogeneous Cauchy problem $$displaylines{ frac{d}{dt}u(t)=A(t)u(t)+f(t), quad 0 leq sleq tleq T, cr L(t)u(t)=Phi(t)u(t)+g(t) , quad 0leq sleq tleq T, cr u(s)=x. }$$ The solution to this problem is obtain...

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Bibliographic Details
Main Authors: Mohammed Filali, Belhadj Karim
Format: Article
Language:English
Published: Texas State University 2006-09-01
Series:Electronic Journal of Differential Equations
Subjects:
Boundary Cauchy problem
evolution families
solution
well posedness
variation of constants formula.
Online Access:http://ejde.math.txstate.edu/conf-proc/14/f1/abstr.html
Description
Summary:In this paper we prove existence and uniqueness of classical solutions for the non-autonomous inhomogeneous Cauchy problem $$displaylines{ frac{d}{dt}u(t)=A(t)u(t)+f(t), quad 0 leq sleq tleq T, cr L(t)u(t)=Phi(t)u(t)+g(t) , quad 0leq sleq tleq T, cr u(s)=x. }$$ The solution to this problem is obtained by a variation of constants formula.
ISSN:1072-6691

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