There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works conc...There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works concern with system which includes more than two terms. In this paper, system which includes four nonlinear terms are studies. We obtain the global asymptotic stability of zero solution, and discard the condition which require the Liapunov function trends to infinity, and only require that the positive orbit is bounded.展开更多
This paper deals with the properties of the solution to a class of nonlocal degenerate reaction-diffusion equation with nonlocal source,subject to the null Dirichlet boundary condition.We first give sufficient conditi...This paper deals with the properties of the solution to a class of nonlocal degenerate reaction-diffusion equation with nonlocal source,subject to the null Dirichlet boundary condition.We first give sufficient conditions for that the solution exists globally or blows up in the finite time.Then the blow-up time is also given.At last,we obtain a property differing from the local source which the blow-up set is the entire interval.展开更多
Mesh-free finite difference(FD)methods can improve the geometric flexibility of modeling without the need for lattice mapping or complex meshing process.Radial-basisfunction-generated FD is among the most commonly use...Mesh-free finite difference(FD)methods can improve the geometric flexibility of modeling without the need for lattice mapping or complex meshing process.Radial-basisfunction-generated FD is among the most commonly used mesh-free FD methods and can accurately simulate seismic wave propagation in the non-rectangular computational domain.In this paper,we propose a perfectly matched layer(PML)boundary condition for a meshfree FD solution of the elastic wave equation,which can be applied to the boundaries of the non-rectangular velocity model.The performance of the PML is,however,severely reduced for near-grazing incident waves and low-frequency waves.We thus also propose the complexfrequency-shifted PML(CFS-PML)boundary condition for a mesh-free FD solution of the elastic wave equation.For two PML boundary conditions,we derive unsplit time-domain expressions by constructing auxiliary differential equations,both of which require less memory and are easy for programming.Numerical experiments demonstrate that these two PML boundary conditions effectively eliminate artificial boundary reflections in mesh-free FD simulations.When compared with the PML boundary condition,the CFS-PML boundary condition results in better absorption for near-grazing incident waves and evanescent waves.展开更多
Lung cancer is one of the most common malignant tumors in the world. Non-small cell lung cancer （NSCLC） accounts for approximately 80% of lung cancer cases, and approximately 75% of patients are diagnosed in the mid...Lung cancer is one of the most common malignant tumors in the world. Non-small cell lung cancer （NSCLC） accounts for approximately 80% of lung cancer cases, and approximately 75% of patients are diagnosed in the middle and late stages. The treatment methods mainly include surgery, chemotherapy, radiotherapy, molecular targeted therapy, traditional Chinese medicine therapy, and immune therapy. We summarize the current status of lung cancer-related treatment options and targets.展开更多
In this paper, we present a new successive approximation damped Newton method for the nonlinear complementarity problem based on its equivalent nonsmooth equations. Under suitable conditions, we obtain the global conv...In this paper, we present a new successive approximation damped Newton method for the nonlinear complementarity problem based on its equivalent nonsmooth equations. Under suitable conditions, we obtain the global convergence result of the proposed algorithms. Some numerical results are also reported.展开更多
A class ofparallel nonlinear multisplitting AOR methods is set upby directly ltisplittingthe nonlinear mapping F:D C Rn、R”for solving the nonlinear system of equationsF(x)= 0.The different choices of the relaxati...A class ofparallel nonlinear multisplitting AOR methods is set upby directly ltisplittingthe nonlinear mapping F:D C Rn、R”for solving the nonlinear system of equationsF(x)= 0.The different choices of the relaxation par。ters c。 yield all the kn。n and a lotof new rel8Xatlon methods as well as a M of new relaxatlon parallel nonlinear multisplittingmethods.Thetwrvsided approximation properties and th IMuences on convergence Mmthe relaxatlon parameters about the new methods are shown,and the sufficient conditionsguaranteeing the methods to converge globally are discussed.FlnallL aht ofnumericalresultsshow that the methods are feasible and efficient.展开更多
In this paper, we prove the global existence and uniqueness of non-negative classical solutions of the Smoluchowski equation with viscosity ε>0. The existence of weak solutions when ε=0 is also obtained.
The exact explicit traveling solutions to the two completely integrable sixthorder nonlinear equations KdV6 are given by using the method of dynamical systems and Cosgrove's work.It is proved that these traveling ...The exact explicit traveling solutions to the two completely integrable sixthorder nonlinear equations KdV6 are given by using the method of dynamical systems and Cosgrove's work.It is proved that these traveling wave solutions correspond to some orbits in the 4-dimensional phase space of two 4-dimensional dynamical systems.These orbits lie in the intersection of two level sets defined by two first integrals.展开更多
文摘There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works concern with system which includes more than two terms. In this paper, system which includes four nonlinear terms are studies. We obtain the global asymptotic stability of zero solution, and discard the condition which require the Liapunov function trends to infinity, and only require that the positive orbit is bounded.
基金Supported by the National Natural Science Foundation of China（10571024）
文摘This paper deals with the properties of the solution to a class of nonlocal degenerate reaction-diffusion equation with nonlocal source,subject to the null Dirichlet boundary condition.We first give sufficient conditions for that the solution exists globally or blows up in the finite time.Then the blow-up time is also given.At last,we obtain a property differing from the local source which the blow-up set is the entire interval.
基金supported by the National Science and Technology Major Project(2016ZX05006-002)the National Natural Science Foundation of China(Nos.41874153,41504097)
文摘Mesh-free finite difference(FD)methods can improve the geometric flexibility of modeling without the need for lattice mapping or complex meshing process.Radial-basisfunction-generated FD is among the most commonly used mesh-free FD methods and can accurately simulate seismic wave propagation in the non-rectangular computational domain.In this paper,we propose a perfectly matched layer(PML)boundary condition for a meshfree FD solution of the elastic wave equation,which can be applied to the boundaries of the non-rectangular velocity model.The performance of the PML is,however,severely reduced for near-grazing incident waves and low-frequency waves.We thus also propose the complexfrequency-shifted PML(CFS-PML)boundary condition for a mesh-free FD solution of the elastic wave equation.For two PML boundary conditions,we derive unsplit time-domain expressions by constructing auxiliary differential equations,both of which require less memory and are easy for programming.Numerical experiments demonstrate that these two PML boundary conditions effectively eliminate artificial boundary reflections in mesh-free FD simulations.When compared with the PML boundary condition,the CFS-PML boundary condition results in better absorption for near-grazing incident waves and evanescent waves.
文摘Lung cancer is one of the most common malignant tumors in the world. Non-small cell lung cancer （NSCLC） accounts for approximately 80% of lung cancer cases, and approximately 75% of patients are diagnosed in the middle and late stages. The treatment methods mainly include surgery, chemotherapy, radiotherapy, molecular targeted therapy, traditional Chinese medicine therapy, and immune therapy. We summarize the current status of lung cancer-related treatment options and targets.
文摘In this paper, we present a new successive approximation damped Newton method for the nonlinear complementarity problem based on its equivalent nonsmooth equations. Under suitable conditions, we obtain the global convergence result of the proposed algorithms. Some numerical results are also reported.
文摘A class ofparallel nonlinear multisplitting AOR methods is set upby directly ltisplittingthe nonlinear mapping F:D C Rn、R”for solving the nonlinear system of equationsF(x)= 0.The different choices of the relaxation par。ters c。 yield all the kn。n and a lotof new rel8Xatlon methods as well as a M of new relaxatlon parallel nonlinear multisplittingmethods.Thetwrvsided approximation properties and th IMuences on convergence Mmthe relaxatlon parameters about the new methods are shown,and the sufficient conditionsguaranteeing the methods to converge globally are discussed.FlnallL aht ofnumericalresultsshow that the methods are feasible and efficient.
基金This research is supported by the National Natural Science Foundation of China
文摘In this paper, we prove the global existence and uniqueness of non-negative classical solutions of the Smoluchowski equation with viscosity ε>0. The existence of weak solutions when ε=0 is also obtained.
基金Project supported by the National Natural Science Foundation of China (Nos.10771196,10831003)the Innovation Project of Zhejiang Province (No.T200905)
文摘The exact explicit traveling solutions to the two completely integrable sixthorder nonlinear equations KdV6 are given by using the method of dynamical systems and Cosgrove's work.It is proved that these traveling wave solutions correspond to some orbits in the 4-dimensional phase space of two 4-dimensional dynamical systems.These orbits lie in the intersection of two level sets defined by two first integrals.
