带非线性边界条件的非线性抛物型方程组

本文讨论带非线性边界条件的抛物型方程组ｕｔ＝Δｕｍ，ｖｔ＝Δｖｍ，ｘ∈Ω，ｔ＞０，ｕｎ＝ｖｐ，ｖｎ＝ｕｑ，ｘ∈Ω，ｔ＞０，ｕ（ｘ，０）＝ｕ０（ｘ）δ＞０，ｖ（ｘ，０）＝ｖ０（ｘ）δ＞０，ｘ∈Ω（Ｉ）解的整体存在性和在有限时刻爆破问题．其中ｍ，ｐ，ｑ＞０，ΩＩＲＮ是有界光滑区域，δ＞０可以充分小．

Nonlinear Parabolic Equations with Nonlinear Boundary Conditions

This paper considers the global existence and blow up problem for the following nonlinear parabolic equations with nonlinear boundary conditionsut =Δum, vt=Δvm, x∈Ω, t>0,un=vp, vn=uq, x∈Ω, t>0,u(x,0)=u0(x)δ>0, v(x,0)=v0(x)δ>0, x∈(I)wherem,p,q>0,ΩRNis a bounded smooth domain,δ>0 maybe small.