Semigroups and linear partial differential equations with delay 半群和线性时滞偏微分方程
Non - linear partial differential equation 偏微分方程式
A symbolic computation method to decide the completeness of the solutions to the system of linear partial differential equations 判定线性偏微分方程组解的完备性的一个符号计算方法
We apply wu - ritt method to linear partial differential equations and gave the size of solution arid formal taylor solutions 我们把它应用到线性偏微分方程上去得到了解的规模和形式幂级数解。
In the first part , by using the method of characteristic curves for solving linear partial differential equations , all invariant algebraic surfaces for three nonlinear systems are obtained 第一部分,利用求解线性偏微分方程的特征曲线法,得到了三个系统的所有不变代数曲面。
In section 1 , the introduction and statement of the main results are stated ; in section 2 , the main tool of this part using is narrated , that is , the method of characteristic curves for solving linear partial differential equations ; in section 3 , rigorous proof is given 本部分由三节组成,第一节是引言和获得的主要结果;第二节介绍了本部分所使用的主要工具,即,解线性偏微分方程的特征曲线法;第三节证明了这些主要结果。
With the method of the lie group transformation , the symmetry of the equation governing one dimensional finite strain consolidation is discussed and , from the point of the symmetry , the feasibility to obtain the analytical solution of these nonlinear partial differential equations is discussed . where - after exact or approximate analytical solutions focused on different consolidation problems are obtained , these including : under some assumptions of relations of the void ratio with coefficient of permeability and effective stress , the method of lie group transformation is applied to solve the non - linear partial differential equation of large strain consolidation of homogenous saturated clay soil in semi - infinite domain with the consideration of the material and geometrical nonlinearity during consolidation procession . the implicit exact solution without considering the effect of self - weight of soil is obtained 运用lie群变换方法讨论了一维大应变非线性固结方程的对称性,以及在该对称性的意义下求解这类非线性偏微分方程解析解答的可能性,并就大应变非线性固结问题的多种情况求得了其完整的或者近似的解析解答,具体包括:基于有效应力与孔隙比以及渗透系数与孔隙比之间的关系的一些假定,采用李群变换求解考虑材料非线性和几何非线性的半无限均质土体大变形固结非线性偏微分方程,得到了一个不考虑自重固结的完全解析解。
The first part , the theory and application about wu - ritt differential characteristic sequence method are discussed , which involves the theories of differential equations , abstract algebra and computer algebra etc . we apply wu - ritt differential characteristic sequence method ( abbr . wu - ritt method ) to linear partial differential equations which has physics significance and give the size of solutions and formal taylor solutions 本文共分两部分,第一部分讨论微分特征列法的理论和应用问题,涉及到微分方程,抽象代数,计算机代数等重要学科。将吴方法应用到具有物理意义的线性偏微分方程上去,我们给出了型序,验证了张鸿庆教授八十年代给出的恰当解的概念,刻划了解的规模并给出了形式幂级数解。
The main result of this part is the following , by using the method of characteristic curves for solving linear partial differential equations , the whole classification of the integrals of motion of the reduced three - wave interaction system is obtained with the condition of some parameters . rigorous proof is given . this part consists of three sections 本部分的主要结论如下,应用解线性偏微分方程的特征曲线法研究了约化的三波相互作用系统的运动积分,给出了在一定参数条件下系统所有的运动积分,并严格证明了这些结论。