@article{Selcuk_2016, title={Quenching problems for a semilinear reaction-diffusion system with singular boundary outflux}, volume={47}, url={https://journals.math.tku.edu.tw/index.php/TKJM/article/view/1961}, DOI={10.5556/j.tkjm.47.2016.1961}, abstractNote={<p>In this paper, we study two quenching problems for the following semilinear reaction-diffusion system:<br />$$u_t=u_{xx}+(1-v)^{-p_1}, 0<x<1,~ 0<t<T,$$<br />$$v_t=v_{xx}+(1-u)^{-p_2}, 0<x<1,~ 0<t<T,$$<br />$$u_x (0,t) =0,~ u_x (1,t) =-v^{-q_1}(1,t),~ 0<t<T,$$<br />$$v_x (0,t) =0,~ v_x (1,t) =-u^{-q_2}(1,t),~ 0<t<T,$$<br />$$u(x,0) =u_0 (x) <1, v( x,0)=v_0 ( x) <1,~  0\le x\le 1,$$<br />where $p_1, p_2, q_1, q_2$ are positive constants and $u_0 (x), v_0 (x)$ 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 $x=0$ and $(u_t ,v_t )$ 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 $x=1$ and $(u_t ,v_t )$ blows up at the quenching time under the certain conditions.</p>}, number={3}, journal={Tamkang Journal of Mathematics}, author={Selcuk, Burhan}, year={2016}, month={Sep.}, pages={323–337} }