International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 4, Pages 775-781
doi:10.1155/S0161171293000961

Solution to a parabolic equation with integral type boundary condition

Ignacio Barradas1 and Salvador Perez-Esteva2

1Centro de Investigatión en Matemáticas, A.C., Apartado Postal 402, Guanajuato Gto. 36000, Mexico
2Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, México, D.F. 04510, Mexico

Received 28 September 1992; Revised 21 January 1993

Copyright © 1993 Ignacio Barradas and Salvador Perez-Esteva. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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).