Smooth Solution of Multi-dimensional Nonhomogeneous Conservation Law : Its Formula, and Necessary and Sufficient Blowup Criterion

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

View graph of relations

Author(s)

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)17-27
Journal / PublicationActa Mathematicae Applicatae Sinica
Volume39
Issue number1
Online published28 Dec 2022
Publication statusPublished - Jan 2023

Abstract

In this paper, we are concerned with the necessary and sufficient condition of the global existence of smooth solutions of the Cauchy problem of the multi-dimensional scalar conservation law with source-term, where the initial data lies in W1,∞(ℝn) ∩ C1(ℝn). We obtain the solution formula for smooth solution, and then apply it to establish and prove the necessary and sufficient condition for the global existence of smooth solution. Moreover, if the smooth solution blows up at a finite time, the exact lifespan of the smooth solution can be obtained. In particular, when the source term vanishes, the corresponding theorem for the homogeneous case is obtained too. Finally, we give two examples as its applications, one for the global existence of the smooth solution and the other one for the blowup of the smooth solutions at any given positive time.

Research Area(s)

  • blowup, global smooth solution, multi-dimensional conservation law, solution formula

Bibliographic Note

Full text of this publication does not contain sufficient affiliation information. With consent from the author(s) concerned, the Research Unit(s) information for this record is based on the existing academic department affiliation of the author(s).

Citation Format(s)