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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/109354


    Title: QUENCHING PROBLEMS FOR A SEMILINEAR REACTION-DIFFUSION SYSTEM WITH SINGULAR BOUNDARY OUTFLUX
    Authors: Selcuk, Burhan
    Keywords: Reaction-diffusion system;singular boundary outflux;quenching;maximum principles;monotone iterations
    Date: 2016-09
    Issue Date: 2017-01-17 09:40:56 (UTC+8)
    Publisher: 淡江大學出版中心
    Abstract: 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.
    Relation: Tamkang Journal of Mathematics 47(3), pp.239-337
    DOI: 10.5556/j.tkjm.47.2016.1961
    Appears in Collections:[淡江數學期刊] 第47卷第3期

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