QUENCHING PROBLEMS FOR A SEMILINEAR REACTION-DIFFUSION SYSTEM WITH SINGULAR BOUNDARY OUTFLUX

淡江大學機構典藏 > 淡江出版期刊 > 淡江數學期刊 > 第47卷第3期 > Item 987654321/109354

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题名:	QUENCHING PROBLEMS FOR A SEMILINEAR REACTION-DIFFUSION SYSTEM WITH SINGULAR BOUNDARY OUTFLUX
作者:	Selcuk, Burhan
关键词:	Reaction-diffusion system;singular boundary outflux;quenching;maximum principles;monotone iterations
日期:	2016-09
上传时间:	2017-01-17 09:40:56 (UTC+8)
出版者:	淡江大學出版中心
摘要:	In this paper, we study two quenching problems for the following semilinear reaction-diffusion system: ut=uxx+(1−v)−p1,0<x<1, 0<t<T,ut=uxx+(1−v)−p1,0<x<1, 0<t<T, vt=vxx+(1−u)−p2,0<x<1, 0<t<T,vt=vxx+(1−u)−p2,0<x<1, 0<t<T, ux(0,t)=0, ux(1,t)=−v−q1(1,t), 0<t<T,ux(0,t)=0, ux(1,t)=−v−q1(1,t), 0<t<T, vx(0,t)=0, vx(1,t)=−u−q2(1,t), 0<t<T,vx(0,t)=0, vx(1,t)=−u−q2(1,t), 0<t<T, u(x,0)=u0(x)<1,v(x,0)=v0(x)<1, 0≤x≤1,u(x,0)=u0(x)<1,v(x,0)=v0(x)<1, 0≤x≤1, where p1,p2,q1,q2p1,p2,q1,q2 are positive constants and u0(x),v0(x)u0(x),v0(x) are positive smooth functions. We firstly get a local exisence result for this system. In the first problem, we show that quenching occurs in finite time, the only quenching point is x=0x=0 and (ut,vt)(ut,vt) blows up at the quenching time under the certain conditions. In the second problem, we show that quenching occurs in finite time, the only quenching point is x=1x=1 and (ut,vt)(ut,vt)blows up at the quenching time under the certain conditions.
關聯:	Tamkang Journal of Mathematics 47(3), pp.239-337
DOI:	10.5556/j.tkjm.47.2016.1961
显示于类别:	[淡江數學期刊] 第47卷第3期

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