Singular points and asymptotics in the singular Cauchy problem for the parabolic equation with a small parameter

DOI10.1134/S0965542520050164zbMath1450.35072OpenAlexW3039100138MaRDI QIDQ2207560

S. V. Zakharov

Publication date: 23 October 2020

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0965542520050164

zbMATH Keywords

self-similarityBurgers equationrenormalizationbisingular problemPearcey functiongradient catastropheweak discontinuityCole-Hopf transformLagrangian singularitymultiscale asymptoticsmethod of matchingWhitney cuspboundary value singularitymerging of shock wavesPoincaré and Erdélyi asymptoticsuniversal Il'in solution

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Initial value problems for second-order parabolic equations (35K15) Quasilinear parabolic equations (35K59)

Related Items (1)

EVOLUTION OF A MULTISCALE SINGULARITY OF THE SOLUTION OF THE BURGERS EQUATION IN THE 4-DIMENSIONAL SPACE–TIME

Cites Work

• Singularities of \(A\) and \(B\) types in asymptotic analysis of solutions of a parabolic equation
• The Cauchy problem for a quasilinear parabolic equation with two small parameters
• Asymptotic solution of the multidimensional Burgers equation near a singularity
• On the critical behavior in nonlinear evolutionary PDEs with small viscosity
• Asymptotic solutions of Navier-Stokes equations and topological invariants of vector fields and Liouville foliations
• Cauchy problem for a quasilinear parabolic equation with a large initial gradient and low viscosity
• Simple viscous flows: From boundary layers to the renormalization group
• Asymptotic behaviour of bounded controls for a singular elliptic problem in a domain with a small cavity
• The renormalization-group method in problems of mechanics
• Shock Waves on the Highway
• The partial differential equation u_t + uu_x = μ_xx
• On kinematic waves II. A theory of traffic flow on long crowded roads
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