带非线性边界条件的非线性抛物型方程组 |
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引用本文: | 王术. 带非线性边界条件的非线性抛物型方程组[J]. 数学学报, 1997, 40(6). DOI: cnki:ISSN:0583-1431.0.1997-06-010 |
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作者姓名: | 王术 |
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作者单位: | 南京大学数学系,河南大学数学系 |
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摘 要: | 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,un=vp,vn=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,ΩIRN是有界光滑区域,δ>0可以充分小.
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关 键 词: | 非线性抛物型方程组,非线性边界条件,整体解,爆破 |
收稿时间: | 1995-06-09 |
修稿时间: | 1996-01-18 |
Nonlinear Parabolic Equations with Nonlinear Boundary Conditions |
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Affiliation: | Wang Shu (Department of Mathematics, Nanjing University, Nanjing 210093, China;)(Department of Mathematics, Henan University, Kaifeng 475001, China)) |
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Abstract: | This paper considers the global existence and blow up problem for the following nonlinear parabolic equations with nonlinear boundary conditionsut =Δum, vt=Δvm, x∈Ω, t>0,un=vp, vn=uq, x∈Ω, t>0,u(x,0)=u0(x)δ>0, v(x,0)=v0(x)δ>0, x∈(I)wherem,p,q>0,ΩRNis a bounded smooth domain,δ>0 maybe small. |
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Keywords: | Nonlinear parabolic equations Nonlinearboundary conditions Global solutions Finite time blow up |
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