According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for geometric...According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for geometrically nonlinear coupled thermoelastodynamics can be established systematically. The new unconventional Hamilton-type variational principle can fully characterize the initial-boundaty-value problem of this dynamics. In this paper, an important integral relation is given, which can be considered as the expression of the generalized principle of virtual work for geometrically nonlinear coupled thermodynamics. Based on this relation, it is possible not only to obtain the principle of virtual work in geometrically nonlinear coupled thermodynamics, but also to derive systematically the complementary functionals for eight-field, six-field, four-field and two-field unconventional Hamilton-type variational principles by the generalized Legendre transformations given in this paper. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly.展开更多
According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for electroma...According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for electromagnetic elastodynamics can be established systematically. This new variational principles can fully characterize the initial-boundary-value problem of this dynamics. In this paper, the expression of the generalized principle of virtual work for electromagnetic dynamics is given. Based on this equation, it is possible not only to obtain the principle of virtual work in electromagnetic dynamics, but also to derive systematically the complementary functionals for eleven-field, nine-field and six-field unconventional Hamilton-type variational principles for electromagnetic elastodynamics, and the potential energy functionals for four-field and three-field ones by the generalized Legendre transformation given in this paper. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly.展开更多
This paper is concerned with a modified transitional Korteweg-de Vries equation ut+f(t)u2ux+uxxx=0, (x,t)∈R+×R+with initial value u(x,0)=g(x)∈H4(R+)and inhomogeneous boundary value u(0,t)=Q(t)∈C2([ 0,∞ )). Un...This paper is concerned with a modified transitional Korteweg-de Vries equation ut+f(t)u2ux+uxxx=0, (x,t)∈R+×R+with initial value u(x,0)=g(x)∈H4(R+)and inhomogeneous boundary value u(0,t)=Q(t)∈C2([ 0,∞ )). Under the conditions either 1) f(t)≤0, f′(t)≥0or 2) f(t)≤−αwhere α>0, we prove the existence of a unique global classical solution.展开更多
基金This work was supported by the National Natural Science Foundation of China (Grant Nos. 10172097, 19672074 & 19902022) Research Grand Council of Hong Kong. No. RGC 97/98, HKUST6055/97E.
文摘According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for geometrically nonlinear coupled thermoelastodynamics can be established systematically. The new unconventional Hamilton-type variational principle can fully characterize the initial-boundaty-value problem of this dynamics. In this paper, an important integral relation is given, which can be considered as the expression of the generalized principle of virtual work for geometrically nonlinear coupled thermodynamics. Based on this relation, it is possible not only to obtain the principle of virtual work in geometrically nonlinear coupled thermodynamics, but also to derive systematically the complementary functionals for eight-field, six-field, four-field and two-field unconventional Hamilton-type variational principles by the generalized Legendre transformations given in this paper. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly.
基金the National Natural Science Foundation of China ( Grant No. 10172097) the Scientific Foundation of the Ministry of Education of China for Doctoral Program ( Grant No. 20030558025).
文摘According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for electromagnetic elastodynamics can be established systematically. This new variational principles can fully characterize the initial-boundary-value problem of this dynamics. In this paper, the expression of the generalized principle of virtual work for electromagnetic dynamics is given. Based on this equation, it is possible not only to obtain the principle of virtual work in electromagnetic dynamics, but also to derive systematically the complementary functionals for eleven-field, nine-field and six-field unconventional Hamilton-type variational principles for electromagnetic elastodynamics, and the potential energy functionals for four-field and three-field ones by the generalized Legendre transformation given in this paper. Furthermore, with this approach, the intrinsic relationship among various principles can be explained clearly.
文摘This paper is concerned with a modified transitional Korteweg-de Vries equation ut+f(t)u2ux+uxxx=0, (x,t)∈R+×R+with initial value u(x,0)=g(x)∈H4(R+)and inhomogeneous boundary value u(0,t)=Q(t)∈C2([ 0,∞ )). Under the conditions either 1) f(t)≤0, f′(t)≥0or 2) f(t)≤−αwhere α>0, we prove the existence of a unique global classical solution.
