非线性对流扩散方程的守恒律  

Conservation laws for nonlinear convection-diffusion equation

作　　者：张俊俊[1] 张隽[1] 

机构地区：[1]浙江工业大学理学院,浙江杭州310023

出　　处：《纯粹数学与应用数学》2016年第3期296-304,共9页Pure and Applied Mathematics

基　　金：国家自然科学基金(11371323);浙江省自然科学基金(Y6100611)

摘　　要：利用直接方法研究了非线性对流扩散方程的守恒律,得到了关于非线性对流扩散方程的守恒律乘子性质的一个定理.利用这个定理,可以简化守恒律乘子的确定方程.随后通过对确定方程中的变量函数进行分析,发现在四种情况下乘子的确定方程是可解的.最后解出这些守恒律乘子,利用积分公式法分别得到了四种情况下对应于各个守恒律乘子的守恒律.In this paper,we use the direct method to study conservation laws for nonlinear convection-diffusion equation and obtain a theorem about the property of the conservation law multipliers for nonlinear convection-diffusion equation. By using this theorem,we can simplify the determining equations of conservation law multipli-ers.Then by analysing variable functions which are in the determining equations,we can find that the determining equations are solvable in four cases. Finally we can get the conservation law multipliers under the four cases by solving the determining equations and obtain the conservation law corresponding to every conservation law multiplier under these four cases by using integral formula method.

关 键 词：非线性对流扩散方程 守恒律乘子 守恒律 欧拉算子 积分公式法 

分 类 号：O175.2[理学—数学]