Geodesic
On some zero-front solutions of an evolution parabolic system
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 224 (2023), pp. 80-88

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We present an existence and uniqueness theorem for a nontrivial analytical zero-front solution of a problem for a nonlinear evolution parabolic predator-prey system. In special cases, we construct exact solutions by reduction to the Cauchy problem for a system of ordinary differential equations, which inherits all features of the original problem. We propose an algorithm for the numerical solution of the problem based on the method of specific solutions and present the result of computational experiments.
Keywords: nonlinear parabolic system, existence theorem, particular solutions method, computational experiment.
Mots-clés : exact solution 
@article{INTO_2023_224_a9,
     author = {A. L. Kazakov and P. A. Kuznetsov and L. F. Spevak},
     title = {On some zero-front solutions of an evolution parabolic system},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {80--88},
     publisher = {mathdoc},
     volume = {224},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_224_a9/}
}
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A. L. Kazakov; P. A. Kuznetsov; L. F. Spevak. On some zero-front solutions of an evolution parabolic system. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 224 (2023), pp. 80-88. http://geodesic.mathdoc.fr/item/INTO_2023_224_a9/