In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficien...In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficient conditions of blow_up of the solution in finite time are given.展开更多
Concerns with the nonexistence of global solutions to the initial boundary value problem for a nonlinear hyperbolic equation with material damping. Nonexitence theorems of global solutions to the above problem are pro...Concerns with the nonexistence of global solutions to the initial boundary value problem for a nonlinear hyperbolic equation with material damping. Nonexitence theorems of global solutions to the above problem are proved by the energy method, Jensen inequality and the concavity method, respectively. As applications of our main results, three examples are given.展开更多
In this paper, we construct a local supersonic flow in a 3-dimensional axis-symmetry nozzle when a uniform supersonic flow inserts the throat. We apply the local existence theory of boundary value problem for quasilin...In this paper, we construct a local supersonic flow in a 3-dimensional axis-symmetry nozzle when a uniform supersonic flow inserts the throat. We apply the local existence theory of boundary value problem for quasilinear hyperbolic system to solve this problem. The boundary value condition is set in particular to guarantee the character number condition. By this trick, the theory in quasilinear hyperbolic system can be employed to a large range of the boundary value problem.展开更多
In this article, we prove that viscosity solutions of the parabolic inhomogeneous equationsn＋p/put-△p^Nu=f（x,t）can be characterized using asymptotic mean value properties for all p ≥ 1, including p = 1 and p = ∞...In this article, we prove that viscosity solutions of the parabolic inhomogeneous equationsn＋p/put-△p^Nu=f（x,t）can be characterized using asymptotic mean value properties for all p ≥ 1, including p = 1 and p = ∞. We also obtain a comparison principle for the non-negative or non-positive inhomogeneous term f for the corresponding initial-boundary value problem and this in turn implies the uniqueness of solutions to such a problem.展开更多
In this paper, the solution, more general than [1], of a weak singular integral equation integral(0)(pi)integral(-infinity)(infinity) p(s,psi)d sk(psi)d psi=F(r,theta), (r,theta)epsilon (Q) over bar=Q+partial derivati...In this paper, the solution, more general than [1], of a weak singular integral equation integral(0)(pi)integral(-infinity)(infinity) p(s,psi)d sk(psi)d psi=F(r,theta), (r,theta)epsilon (Q) over bar=Q+partial derivative Q subject to constraint p(s,psi)=0, for (s,psi)=(r,theta)is not an element of Q={r,theta)/F(r,theta)>c*} is found p=2/pi[root w g'(0)+integral(0)(w) root w-u g '(u)du] where k and F are given continuous functions; (s,psi) is a local polar coordinating with origin at M(r,theta); (r,theta) is the global polar coordinating with origin at O(0,0) F(r,theta)=c* (const.) is the boundary contour partial derivative Q of the considered range Q; g(w)=F(r,theta)/[pi k(psi(0))]; g'=dg/dw; w=N-r(2)sin(2)(theta+psi(0)); psi(0) and N are mean values. The solution shown in type (2.19) of [1] is a special case of the above solution and only suits F(r,theta)=w. The solution of a rigid cone contact with elastic half space, more simple and clear than Love's (1939), is given as an example of application.展开更多
We establish a new type of backward stochastic differential equations(BSDEs)connected with stochastic differential games(SDGs), namely, BSDEs strongly coupled with the lower and the upper value functions of SDGs, wher...We establish a new type of backward stochastic differential equations(BSDEs)connected with stochastic differential games(SDGs), namely, BSDEs strongly coupled with the lower and the upper value functions of SDGs, where the lower and the upper value functions are defined through this BSDE. The existence and the uniqueness theorem and comparison theorem are proved for such equations with the help of an iteration method. We also show that the lower and the upper value functions satisfy the dynamic programming principle. Moreover, we study the associated Hamilton-Jacobi-Bellman-Isaacs(HJB-Isaacs)equations, which are nonlocal, and strongly coupled with the lower and the upper value functions. Using a new method, we characterize the pair(W, U) consisting of the lower and the upper value functions as the unique viscosity solution of our nonlocal HJB-Isaacs equation. Furthermore, the game has a value under the Isaacs’ condition.展开更多
For a family of linear hyperbolic damped stochastic wave equations with rapidly oscillating coefficients, we establish the homogenization result by using the sigma-convergence method. This is achieved under an abstrac...For a family of linear hyperbolic damped stochastic wave equations with rapidly oscillating coefficients, we establish the homogenization result by using the sigma-convergence method. This is achieved under an abstract assumption covering special cases like the periodicity, the almost periodicity and some others.展开更多
文摘In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficient conditions of blow_up of the solution in finite time are given.
基金Project supported by the National Natural Science Foundation of China (Nos. 10371073 and 10572156) the Natural Science Foundation of Henan Province of China (No.0611050500)
文摘Concerns with the nonexistence of global solutions to the initial boundary value problem for a nonlinear hyperbolic equation with material damping. Nonexitence theorems of global solutions to the above problem are proved by the energy method, Jensen inequality and the concavity method, respectively. As applications of our main results, three examples are given.
文摘In this paper, we construct a local supersonic flow in a 3-dimensional axis-symmetry nozzle when a uniform supersonic flow inserts the throat. We apply the local existence theory of boundary value problem for quasilinear hyperbolic system to solve this problem. The boundary value condition is set in particular to guarantee the character number condition. By this trick, the theory in quasilinear hyperbolic system can be employed to a large range of the boundary value problem.
基金supported by the National Natural Science Foundation of China(11071119,11171153)
文摘In this article, we prove that viscosity solutions of the parabolic inhomogeneous equationsn＋p/put-△p^Nu=f（x,t）can be characterized using asymptotic mean value properties for all p ≥ 1, including p = 1 and p = ∞. We also obtain a comparison principle for the non-negative or non-positive inhomogeneous term f for the corresponding initial-boundary value problem and this in turn implies the uniqueness of solutions to such a problem.
文摘In this paper, the solution, more general than [1], of a weak singular integral equation integral(0)(pi)integral(-infinity)(infinity) p(s,psi)d sk(psi)d psi=F(r,theta), (r,theta)epsilon (Q) over bar=Q+partial derivative Q subject to constraint p(s,psi)=0, for (s,psi)=(r,theta)is not an element of Q={r,theta)/F(r,theta)>c*} is found p=2/pi[root w g'(0)+integral(0)(w) root w-u g '(u)du] where k and F are given continuous functions; (s,psi) is a local polar coordinating with origin at M(r,theta); (r,theta) is the global polar coordinating with origin at O(0,0) F(r,theta)=c* (const.) is the boundary contour partial derivative Q of the considered range Q; g(w)=F(r,theta)/[pi k(psi(0))]; g'=dg/dw; w=N-r(2)sin(2)(theta+psi(0)); psi(0) and N are mean values. The solution shown in type (2.19) of [1] is a special case of the above solution and only suits F(r,theta)=w. The solution of a rigid cone contact with elastic half space, more simple and clear than Love's (1939), is given as an example of application.
基金supported by the NSF of China(11071144,11171187,11222110 and 71671104)Shandong Province(BS2011SF010,JQ201202)+4 种基金SRF for ROCS(SEM)Program for New Century Excellent Talents in University(NCET-12-0331)111 Project(B12023)the Ministry of Education of Humanities and Social Science Project(16YJA910003)Incubation Group Project of Financial Statistics and Risk Management of SDUFE
文摘We establish a new type of backward stochastic differential equations(BSDEs)connected with stochastic differential games(SDGs), namely, BSDEs strongly coupled with the lower and the upper value functions of SDGs, where the lower and the upper value functions are defined through this BSDE. The existence and the uniqueness theorem and comparison theorem are proved for such equations with the help of an iteration method. We also show that the lower and the upper value functions satisfy the dynamic programming principle. Moreover, we study the associated Hamilton-Jacobi-Bellman-Isaacs(HJB-Isaacs)equations, which are nonlocal, and strongly coupled with the lower and the upper value functions. Using a new method, we characterize the pair(W, U) consisting of the lower and the upper value functions as the unique viscosity solution of our nonlocal HJB-Isaacs equation. Furthermore, the game has a value under the Isaacs’ condition.
基金the support of the CETIC(African Center of Excellence in Information and Communication Technologies)the support of the Humboldt Foundation
文摘For a family of linear hyperbolic damped stochastic wave equations with rapidly oscillating coefficients, we establish the homogenization result by using the sigma-convergence method. This is achieved under an abstract assumption covering special cases like the periodicity, the almost periodicity and some others.
