一类小参数退化抛物型方程基本解的精确渐近性

IF 1.5 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2025-07-29 DOI:10.1134/S1061920825600722

M.A. Rakhel

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引用次数: 0

摘要

本文构造了一类具有小参数的退化抛物型方程在最高导数处的基本解的渐近性。结果表明，渐近的前项包含两个相函数，这对于线性问题来说是不典型的。给出了一般情况下渐近的前导项与平凡情况下的精确解之间的估计。渐近函数以小参数幂级数的形式构造。通过证明所得级数的收敛性来证明渐近性。DOI 10.1134 / S1061920825600722

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Exact Asymptotics of the Fundamental Solution of a Degenerate Parabolic Equation with a Small Parameter

In this paper, the asymptotics of the fundamental solution of a degenerate parabolic equation with a small parameter at the highest derivative is constructed. It is shown that the leading term of the asymptotics contains two phase functions, which is not typical for linear problems. Estimates are provided that relate the leading term of the asymptotics in the general case to the exact solution in the trivial case. The asymptotics is constructed in the form of a formal series in powers of the small parameter. The asymptotics is justified by proving the convergence of the obtained series.

DOI 10.1134/S1061920825600722

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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.