Article ID Journal Published Year Pages File Type
4619342 Journal of Mathematical Analysis and Applications 2010 10 Pages PDF
Abstract

We consider the initial–boundary value problem for the heat equation with a nonlinear boundary condition:{∂tu=Δu,x∈R+N,t>0,u(x,0)=φ(x),x∈R+N,−∂u∂xN=up,x∈∂R+N,t>0, where N⩾1N⩾1, p>1+1/Np>1+1/N, and φ∈L1(R+N)∩L∞(R+N). We prove the existence of global solutions with a small initial data, and study the large time behavior of solutions.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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