Geodesic
Solution of nonlinear partial differential equations by the geometric method
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 2, pp. 265-280 Cet article a éte moissonné depuis la source Math-Net.Ru

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The earlier proposed geometric method of investigation of nonlinear partial differential equations is developed. The heat equation describing blow-up regimes and the equation for the flow function in a boundary layer are studied. We propose a modification of the method based on the specific character of the equations and show its applicability in the case under consideration. Classes of particular exact solutions are found and a boundary value problem is solved.
Keywords: nonlinear partial differential equations, heat equation, equation for the flow function in a boundary layer
Mots-clés : exact solutions. 
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L. I. Rubina; O. N. Ul'yanov. Solution of nonlinear partial differential equations by the geometric method. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 2, pp. 265-280. http://geodesic.mathdoc.fr/item/TIMM_2012_18_2_a25/

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