Well-Posedness of Nonlocal Parabolic Differential Problems with Dependent Operators - Allaberen Ashyralyev; Asker Hanalyev (The Scientific World Journal)
The nonlocal boundary value problem for the parabolic differential equation v'(t)+A(t)v(t)=f(t)  (0≤t≤T),  v(0)=v(λ)+φ,  0<λ≤T in an arbitrary Banach space E with the dependent linear positive operator A(t) is investigated. The well-posedness of this problem is established in Banach spaces C0β,γ(Eα-β) of all Eα-β-valued continuous functions φ(t) on [0,T] satisfying a Hölder condition with a weight (t+τ)γ. New Schauder type exact estimates in Hölder norms for the solution of two nonlocal boundary value problems for parabolic equations with dependent coefficients are established.