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- Title
On Asymptotics of the Solution to the Cauchy Problem for a Singularly Perturbed Operator-Differential Transport Equation with Weak Diffusion in the Case of Several Space Variables.
- Authors
Nesterov, A. V.
- Abstract
A formal asymptotic expansion is constructed for the solution of the Cauchy problem for a singularly perturbed operator differential transport equation with small nonlinearities and weak diffusion in the case of several space variables. Under the conditions imposed on the data of the problem, the leading asymptotic term is described by the multidimensional generalized Burgers–Korteweg–de Vries equation. Under certain conditions, the remainder is estimated with respect to the residual.
- Subjects
CAUCHY problem; TRANSPORT equation; DIFFERENTIAL-difference equations; HEAT equation; ASYMPTOTIC expansions; DIFFERENTIAL operators; DIFFERENTIAL equations
- Publication
Computational Mathematics & Mathematical Physics, 2024, Vol 64, Issue 3, p490
- ISSN
0965-5425
- Publication type
Article
- DOI
10.1134/S0965542524030114