Non-autonomous inhomogeneous boundary Cauchy problems

• 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

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.