Existence of classical solutions to nonautonomous nonlocal parabolic problems Original Research Article

We obtain a new existence theorem for classical solutions to nonautonomous equations with nonlocal initial conditions View the MathML sourceu′(t)=A(t)u(t)+f(t,u(t)),t∈(s,T],u(s)+g(u)=u0, Turn MathJax on in a Banach space X, where T>s⩾0T>s⩾0, View the MathML sourcef,g are given X-valued functions, and A(t)A(t) is a sectorial operator (not necessarily densely defined) in X for each t∈[0,T]t∈[0,T]. Both Banachʹs contraction principle and Schauderʹs fixed point theorem, as well as the theory of evolution families and interpolation spaces, are employed in our approach. A concrete example is shown to illustrate the existence theorem.