## THERMAL SCIENCE

International Scientific Journal

### CONSERVATION LAWS FOR PARTIAL DIFFERENTIAL EQUATIONS BASED ON THE POLYNOMIAL CHARACTERISTIC METHOD

**ABSTRACT**

In this paper, the direct construction method combined with the differential polynomial characteristic set algorithm is used to complete conservation laws of PDE. The process of the direct construction method is to solve a system of linear determining equations, which is not easy to be solved. This paper uses the differential polynomial characteristic set algorithm to overcome the shortcoming, and constructs an explicit conservation law.

**KEYWORDS**

PAPER SUBMITTED: 2019-03-23

PAPER REVISED: 2019-10-20

PAPER ACCEPTED: 2019-10-21

PUBLISHED ONLINE: 2020-06-21

**THERMAL SCIENCE** YEAR

**2020**, VOLUME

**24**, ISSUE

**4**, PAGES [2529 - 2534]

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