Geodesic
On one class of exact solutions of the multidimensional nonlinear heat equation with a zero front
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 5th International Conference "Dynamical Systems and Computer Science: Theory and Applications" (DYSC 2023). Irkutsk, September 18-23, 2023, Tome 234 (2024), pp. 59-66

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We consider a class of exact solutions of a multidimensional nonlinear heat equation with a source. The construction of these solutions leads to the solution of a family of second-order ordinary differential equations. If appropriate Cauchy conditions are specified, exact solutions can be interpreted as nontrivial solutions with zero front. An existence theorem is proved and a solution is constructed in the form of a converging power series. An approximate algorithm based on the collocation method of radial basis functions is proposed. Test calculations and numerical analysis of the solutions obtained are performed.
Keywords: nonlinear parabolic system, existence theorem, collocation method, radial basic functions, numerical analysis
Mots-clés : exact solution 
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     title = {On one class of exact solutions of the multidimensional nonlinear heat equation with a zero front},
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     volume = {234},
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A. L. Kazakov; L. F. Spevak. On one class of exact solutions of the multidimensional nonlinear heat equation with a zero front. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 5th International Conference "Dynamical Systems and Computer Science: Theory and Applications" (DYSC 2023). Irkutsk, September 18-23, 2023, Tome 234 (2024), pp. 59-66. http://geodesic.mathdoc.fr/item/INTO_2024_234_a7/