双曲齐次标量一维守恒律的显式解

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-04-29 DOI:10.1016/j.aml.2025.109593

Didier Clamond

引用次数: 0

摘要

对于任意通量f(u)和初始条件u0(x)为解析型的非线性标量一维方程ut+[f(u)]x=0，用复积分公式给出了初值问题的显式解。这个公式对某些时刻t>；0有效，但仍然是解析式的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Explicit solution for the hyperbolic homogeneous scalar one-dimensional conservation law

A complex integral formula provides an explicit solution of the initial value problem for the nonlinear scalar 1D equation

u_{t} + {[f (u)]}_{x} = 0

, for any flux

f (u)

and initial condition

u_{0} (x)

that are analytic. This formula is valid for some times

t > 0

u

remaining analytic.

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.