On the resolution of a parabolic equation in a nonregular domain of ℝ^3

Abstract

In this work we give new results of existence , uniqueness and maximal regularity of a solution to a parabolic equation set in a nonregular domain Q with Cauchy-Dirichlet boundary conditions, where Q = � (t,x1) ∈ R 2 :0 <t < T;ϕ1(t) < x1 < ϕ2(t) � ×)0,b( ⊆ R 3 with some assumptions on the functions (ϕi)i=1,2. The right-hand side term of the equation is taken in L 2 (Q) . The method used is based on the approximation of the domain Q by a sequence of subdomains (Qn)n which can be transformed into regular domains . This work is an extension of the one space variable case studied in (12).