Geodesic
Asymptotic solution of the~multidimensional Burgers equation near a~singularity
Teoretičeskaâ i matematičeskaâ fizika, Tome 196 (2018) no. 1, pp. 42-49

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We consider the Cauchy problem for the multidimensional Burgers equation with a small dissipation parameter and use the matching method to construct an asymptotic solution near the singularity determined by the vector field structure at the initial instant. The method that we use allows tracing the evolution of the solution with a hierarchy of differently scaled structures and giving a rigorous mathematical definition of the asymptotic solution in the leading approximation. We discuss the relation of the considered problem to different models in fundamental and applied physics.
Keywords: multidimensional Burgers equation, Cauchy problem, asymptotics. 
@article{TMF_2018_196_1_a3,
     author = {S. V. Zakharov},
     title = {Asymptotic solution of the~multidimensional {Burgers} equation near a~singularity},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {42--49},
     publisher = {mathdoc},
     volume = {196},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_196_1_a3/}
}
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S. V. Zakharov. Asymptotic solution of the~multidimensional Burgers equation near a~singularity. Teoretičeskaâ i matematičeskaâ fizika, Tome 196 (2018) no. 1, pp. 42-49. http://geodesic.mathdoc.fr/item/TMF_2018_196_1_a3/