Group classification of quasilinear third-order evolution equations is given by using the classical infinitesimal Lie method, the technique of equivalence transformations, and the theory of classification of abstract ...Group classification of quasilinear third-order evolution equations is given by using the classical infinitesimal Lie method, the technique of equivalence transformations, and the theory of classification of abstract low-dimensional Lie algebras. We show that there are three equations admitting simple Lie algebras of dimension three. All non-equivalent equations admitting simple Lie algebras are nothing but these three. Furthermore, we also show that there exist two, five, twenty-nine and twenty-six non- equivalent third-order nonlinear evolution equations admitting one-, two-, three-, and four-dimensional solvable Lie algebras, respectively.展开更多
This is the third part of the papers with the same title. We will discuss the problem of convergence of the semi-implicit difference scheme for a class of quasilinear SEE, which generalize the Crandall's work to t...This is the third part of the papers with the same title. We will discuss the problem of convergence of the semi-implicit difference scheme for a class of quasilinear SEE, which generalize the Crandall's work to the stochastic case.展开更多
The author proves a global existence result for strong solutions to the quasilinear dissipative hyperbolic equation (1.1) below, corresponding to initial values and source terms of arbitrary size, provided that the hy...The author proves a global existence result for strong solutions to the quasilinear dissipative hyperbolic equation (1.1) below, corresponding to initial values and source terms of arbitrary size, provided that the hyperbolicity parameter ε is sufficiently small. This implies a corresponding global existence result for the reduced quasilinear parabolic equation (1.4) below.展开更多
基金supported by the National Key Basic Research Project of China (973 Program)(No. 2004CB318000)
文摘Group classification of quasilinear third-order evolution equations is given by using the classical infinitesimal Lie method, the technique of equivalence transformations, and the theory of classification of abstract low-dimensional Lie algebras. We show that there are three equations admitting simple Lie algebras of dimension three. All non-equivalent equations admitting simple Lie algebras are nothing but these three. Furthermore, we also show that there exist two, five, twenty-nine and twenty-six non- equivalent third-order nonlinear evolution equations admitting one-, two-, three-, and four-dimensional solvable Lie algebras, respectively.
基金Work supported by National Natural Science Foundation of China.
文摘This is the third part of the papers with the same title. We will discuss the problem of convergence of the semi-implicit difference scheme for a class of quasilinear SEE, which generalize the Crandall's work to the stochastic case.
基金supported by the Fulbright Foundation (Chile, 2006)
文摘The author proves a global existence result for strong solutions to the quasilinear dissipative hyperbolic equation (1.1) below, corresponding to initial values and source terms of arbitrary size, provided that the hyperbolicity parameter ε is sufficiently small. This implies a corresponding global existence result for the reduced quasilinear parabolic equation (1.4) below.
