%0 Journal Article
%T Existence and uniqueness of generalized solution of two point nonlocal boundary conditions of second mixed problem for second order linear parabolic equation
%A M. Z. Djibibe
%J International Mathematical Forum
%D 2013
%I 
%X The aim of this paper is to prove existence and uniqueness of a generalized solution for certain parabolic equations with initial and nonlocal boundary conditions : begin{align*}begin{cases}&dfrac{partial v}{partial t} - a(x, t)dfrac{partial^2 u}{partial x^2} + b(x, t)dfrac{partial v}{partial x} + c(x, t) v =f(x, t)&&v(x, 0) = varphi(x), 0leq xleq ell&&v(0,t) =psi(t), 0leq tleq T&&displaystyle{int_0^Tfrac{v^2(ell, t) -v^2(xi, t)}{ell -xi} },dt = 0, 0< xi < ellend{cases}end{align*}The proofs are based on a priori estimates established in non-classical function spaces and on the density of the range of the operator corresponding to the abstract formulation of the considered problem.
%K Parabolic equation
%K Nonlocal conditions
%K a Priori estimate
%K Generalized solution
%K Two points
%U http://www.m-hikari.com/imf/imf-2013/1-4-2013/djibibeIMF1-4-2013.pdf