Solution to a parabolic equation with integral type boundary condition

Abstract

In this paper we study the existence, and continuous dependence of the solution ϑ=ϑ(x,t) on a Hölder space H2+γ,1+γ/2(Q¯τ)(Q¯τ=[0,1]×[0,τ],   0<γ<1) of a linear parabolic equation, prescribing ϑ(x,0)=f(x), ϑx(1,τ)=g(τ) the integral type condition ∫0bϑ(x,τ)dx=E(τ).