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A reaction-diffusion system with fast reversible reaction. (English) Zbl 1039.35013
The authors study a diffusion-reaction system of the form \begin{aligned} u_t &= d_1\Delta u-\alpha k(r_A(u)- r_B(v)),\\ v_t &= d_2\Delta v+\beta k(r_A(u)- r_B(v))\end{aligned} in a bounded domain with no-flux boundary conditions. Here $$\alpha$$, $$\beta$$, $$k> 0$$.
They prove an interesting result concerning the limiting behaviour of $$(u,v)$$ as $$k\to \infty$$.

MSC:
 35B25 Singular perturbations in context of PDEs 35K57 Reaction-diffusion equations 35K50 Systems of parabolic equations, boundary value problems (MSC2000)
Keywords:
no-flux boundary conditions
Full Text:
References:
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