Asymptotic Solutions of a Parabolic Equation Near Singular Points of A and B Types

DOI10.15826/umj.2019.1.010zbMath1448.35023OpenAlexW2965314442MaRDI QIDQ5125234

S. V. Zakharov

Publication date: 5 October 2020

Published in: Ural Mathematical Journal (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/umj78

zbMATH Keywords

weighted Sobolev spacesCole-Hopf transformIl'in's universal solutionWhitney fold singularity

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Initial value problems for second-order parabolic equations (35K15) Semilinear parabolic equations (35K58)

Cites Work

• Singularities of \(A\) and \(B\) types in asymptotic analysis of solutions of a parabolic equation
• Asymptotic solution of the multidimensional Burgers equation near a singularity
• Normal forms for functions near degenerate critical points, the Weyl groups of A\(_k\), D\(_k\), E\(_k\) and lagrangian singularities
• Shock waves for the Burgers equation and curvatures of diffeomorphism groups
• CRITICAL POINTS OF FUNCTIONS ON A MANIFOLD WITH BOUNDARY, THE SIMPLE LIE GROUPSB_k,C_k, ANDF₄AND SINGULARITIES OF EVOLUTES
• Asymptotic solution of a Cauchy problem in a neighbourhood of a gradient catastrophe
• From weak discontinuity to gradient catastrophe
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