Geodesic
Time-independent reaction-diffusion equation with a discontinuous reactive term
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 5, pp. 854-866

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A two-dimensional singularly perturbed elliptic equation referred to in applications as the reaction-diffusion equation is considered. The nonlinearity describing the reaction is assumed to be discontinuous on a certain closed curve. On the basis of the generalized asymptotic comparison principle, the existence of smooth solution is proven and the accuracy of the asymptotic approximation is estimated. 
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     author = {N. T. Levashova and N. N. Nefedov and A. O. Orlov},
     title = {Time-independent reaction-diffusion equation with a discontinuous reactive term},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
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     number = {5},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_5_a7/}
}
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N. T. Levashova; N. N. Nefedov; A. O. Orlov. Time-independent reaction-diffusion equation with a discontinuous reactive term. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 5, pp. 854-866. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_5_a7/