Parabolic problems with nonlinear absorptions and releases at the boundaries

摘要

Let a,p and q be positive constants, T⩽∞, D=(0,a), D̄ be the closure of D, Ω=D×(0,T), and Hu≡ut−uxx. This article studies the following heat conduction problem with nonlinear boundary conditions:Hu=0inΩ,u(x,0)=u0(x)onD̄,ux(0,t)=(1−u(0,t))−p,ux(a,t)=(1−u(a,t))−q,0