In this paper,we investigate the strong Feller property of stochastic differential equations(SDEs)with super-linear drift and Hölder diffusion coefficients.By utilizing the Girsanov theorem,coupling method,trunca...In this paper,we investigate the strong Feller property of stochastic differential equations(SDEs)with super-linear drift and Hölder diffusion coefficients.By utilizing the Girsanov theorem,coupling method,truncation method and the Yamada-Watanabe approximation technique,we derived the strong Feller property of the solution.展开更多
A boundary element method based on non-overlapping domain decomposition method to solve the time-dependent diffusion equations is presented. The time-dependent fundamental solution is used in the formulation of bounda...A boundary element method based on non-overlapping domain decomposition method to solve the time-dependent diffusion equations is presented. The time-dependent fundamental solution is used in the formulation of boundary integrals and the time integration process always restarts from the initial time condition. The process of replacing the interface values, which needs a summation of boundary integrals related to the boundary values at previous time steps can be treated in parallel iterative procedure. Numerical experiments demonstrate that the implementation of the present algorithm is efficient.展开更多
In this paper, we investigate conservation laws of a class of partial differential equations, which combines the nonlinear telegraph equations and the nonlinear diffusion-convection equations. Moreover, some special c...In this paper, we investigate conservation laws of a class of partial differential equations, which combines the nonlinear telegraph equations and the nonlinear diffusion-convection equations. Moreover, some special conservation laws of the combined equations are obtained by means of symmetry classifications of wave equations uxx = H （x）utt.展开更多
In this article, we consider a reaction-diffusion differential equation with initial value conditions u（x, 0） =0 on [0, a] and boundary condition ux＋αiu= 0 on Γ={0, α}× （0, T）, and the quenching happens f...In this article, we consider a reaction-diffusion differential equation with initial value conditions u（x, 0） =0 on [0, a] and boundary condition ux＋αiu= 0 on Γ={0, α}× （0, T）, and the quenching happens for the reaction-diffusion equation.展开更多
In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations....In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations. With the aid of symbolic computation, we apply the proposed method to solving the (1+1)-dimensional dispersive long wave equation and explicitly construct a series of exact solutions which include the rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases.展开更多
This paper introduces the use of partition of unity method for the development of a high order finite volume discretization scheme on unstructured grids for solving diffusion models based on partial differential equat...This paper introduces the use of partition of unity method for the development of a high order finite volume discretization scheme on unstructured grids for solving diffusion models based on partial differential equations.The unknown function and its gradient can be accurately reconstructed using high order optimal recovery based on radial basis functions.The methodology proposed is applied to the noise removal problem in functional surfaces and images.Numerical results demonstrate the effectiveness of the new numerical approach and provide experimental order of convergence.展开更多
In this paper,an orthogonal-directional forward diffusion Partial Differential Equation(PDE) image inpainting and denoising model which processes image based on variation problem is proposed.The novel model restores t...In this paper,an orthogonal-directional forward diffusion Partial Differential Equation(PDE) image inpainting and denoising model which processes image based on variation problem is proposed.The novel model restores the damaged information and smoothes the noise in image si-multaneously.The model is morphological invariant which processes image based on the geometrical property.The regularization item of it diffuses along and cross the isophote,and then the known image information is transported into the target region through two orthogonal directions.The cross isophote diffusion part is the TV(Total Variation) equation and the along isophote diffusion part is the inviscid Helmholtz vorticity equation.The equivalence between the Helmholtz equation and the inpainting PDEs is proved.The model with the fidelity item which is used in the whole image domain denoises while preserving edges.So the novel model could inpaint and denoise simultaneously.Both theoretical analysis and experiments have verified the validity of the novel model proposed in this paper.展开更多
In this paper, blow-up estimates for a class of quasiliuear reaction-diffusion equations(non-Newtonian filtration equations) in term of the nouexistence result for quasilinear ordinary differential equations are estab...In this paper, blow-up estimates for a class of quasiliuear reaction-diffusion equations(non-Newtonian filtration equations) in term of the nouexistence result for quasilinear ordinary differential equations are established to extends the result for semi-linear reaction-diffusion equations(Newtonian filtration equations).展开更多
Dynamical characteristics of an integrodifferential modelling competitive sys-tem with diffusion are investigated.In particular,we derive sufficient conditions for the permanence of species,existence of an attracting ...Dynamical characteristics of an integrodifferential modelling competitive sys-tem with diffusion are investigated.In particular,we derive sufficient conditions for the permanence of species,existence of an attracting periodic solution to the periodic system.The results of Wang Ke in 1994 and 1998 are improved and extended.展开更多
A class of differential-difference reaction diffusion equations with a small time delay is considered.Under suitable conditions and by using the method of the stretched variable,the formal asymptotic solution is const...A class of differential-difference reaction diffusion equations with a small time delay is considered.Under suitable conditions and by using the method of the stretched variable,the formal asymptotic solution is constructed.And then,by using the theory of differential inequalities the uniformly validity of solution is proved.展开更多
In the one-dimensional space, traveling wave solutions of parabolic differential equations have been widely studied and well characterized. Recently, the mathematical study on higher-dimensional traveling fronts has a...In the one-dimensional space, traveling wave solutions of parabolic differential equations have been widely studied and well characterized. Recently, the mathematical study on higher-dimensional traveling fronts has attracted a lot of attention and many new types of nonplanar traveling waves have been observed for scalar reaction-diffusion equations with various nonlinearities. In this paper, by using the comparison argument and constructing appropriate super- and subsolutions, we study the existence, uniqueness and stability of three- dimensional traveling fronts of pyramidal shape for monotone bistable systems of reaction-diffusion equations in R3. The pyramidal traveling fronts are characterized as either a combination of planar traveling fronts on the lateral surfaces or a combination of two-dimensional V-form waves on the edges of the pyramid. In particular, our results are applicable to some important models in biology, such as Lotk,u-Volterra competition-diffusion systems with or without spatio-temporal delays, and reaction-diffusion systems of multiple obligate mutualists.展开更多
On the basis of Lie group theory,(1 + N)-dimensional time-fractional partial differential equations are studied and the expression of η_α~0 is given. As applications, two special forms of nonlinear time-fractional d...On the basis of Lie group theory,(1 + N)-dimensional time-fractional partial differential equations are studied and the expression of η_α~0 is given. As applications, two special forms of nonlinear time-fractional diffusionconvection equations are investigated by Lie group analysis method. Then the equations are reduced into fractional ordinary differential equations under group transformations. Therefore, the invariant solutions and some exact solutions are obtained.展开更多
基金Supported by the National Natural Science Foundation of China(11926322)the Fundamental Research Funds for the Central Universities of South-Central MinZu University(CZY22013,3212023sycxjj001)。
文摘In this paper,we investigate the strong Feller property of stochastic differential equations(SDEs)with super-linear drift and Hölder diffusion coefficients.By utilizing the Girsanov theorem,coupling method,truncation method and the Yamada-Watanabe approximation technique,we derived the strong Feller property of the solution.
文摘A boundary element method based on non-overlapping domain decomposition method to solve the time-dependent diffusion equations is presented. The time-dependent fundamental solution is used in the formulation of boundary integrals and the time integration process always restarts from the initial time condition. The process of replacing the interface values, which needs a summation of boundary integrals related to the boundary values at previous time steps can be treated in parallel iterative procedure. Numerical experiments demonstrate that the implementation of the present algorithm is efficient.
文摘In this paper, we investigate conservation laws of a class of partial differential equations, which combines the nonlinear telegraph equations and the nonlinear diffusion-convection equations. Moreover, some special conservation laws of the combined equations are obtained by means of symmetry classifications of wave equations uxx = H （x）utt.
文摘In this article, we consider a reaction-diffusion differential equation with initial value conditions u（x, 0） =0 on [0, a] and boundary condition ux＋αiu= 0 on Γ={0, α}× （0, T）, and the quenching happens for the reaction-diffusion equation.
文摘In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations. With the aid of symbolic computation, we apply the proposed method to solving the (1+1)-dimensional dispersive long wave equation and explicitly construct a series of exact solutions which include the rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases.
基金supported by PRIN-MIUR-Cofin 2006by University of Bologna"Funds for selected research topics"
文摘This paper introduces the use of partition of unity method for the development of a high order finite volume discretization scheme on unstructured grids for solving diffusion models based on partial differential equations.The unknown function and its gradient can be accurately reconstructed using high order optimal recovery based on radial basis functions.The methodology proposed is applied to the noise removal problem in functional surfaces and images.Numerical results demonstrate the effectiveness of the new numerical approach and provide experimental order of convergence.
基金the National Natural Science Foundation of China(No.60472033, No.60672062)the National Grand Fundamental Research 973 Program of China(No. 2004CB318005)the Technological Innovation Fund of Excellent Doctorial Candidate of Beijing Jiaotong University(No.48026)
文摘In this paper,an orthogonal-directional forward diffusion Partial Differential Equation(PDE) image inpainting and denoising model which processes image based on variation problem is proposed.The novel model restores the damaged information and smoothes the noise in image si-multaneously.The model is morphological invariant which processes image based on the geometrical property.The regularization item of it diffuses along and cross the isophote,and then the known image information is transported into the target region through two orthogonal directions.The cross isophote diffusion part is the TV(Total Variation) equation and the along isophote diffusion part is the inviscid Helmholtz vorticity equation.The equivalence between the Helmholtz equation and the inpainting PDEs is proved.The model with the fidelity item which is used in the whole image domain denoises while preserving edges.So the novel model could inpaint and denoise simultaneously.Both theoretical analysis and experiments have verified the validity of the novel model proposed in this paper.
基金Supported by the National Natural Science Foundation of China(10172011)
文摘In this paper, blow-up estimates for a class of quasiliuear reaction-diffusion equations(non-Newtonian filtration equations) in term of the nouexistence result for quasilinear ordinary differential equations are established to extends the result for semi-linear reaction-diffusion equations(Newtonian filtration equations).
基金This research is supported by the National Natural Science Foundation of China.
文摘Dynamical characteristics of an integrodifferential modelling competitive sys-tem with diffusion are investigated.In particular,we derive sufficient conditions for the permanence of species,existence of an attracting periodic solution to the periodic system.The results of Wang Ke in 1994 and 1998 are improved and extended.
基金the National Natural Science Foundation of China (Nos.40676016 and 40876010)the National Basic Research Program (973) of China (Nos.2003CB415101-03 and 2004CB418304)+2 种基金the Knowledge Innovation Project of Chinese Academy of Sciences (No.KZCX2-YW-Q03-08)LASG State Key Laboratory Special FundE-Institutes of Shanghai Municipal Education Commission (No.E03004)
文摘A class of differential-difference reaction diffusion equations with a small time delay is considered.Under suitable conditions and by using the method of the stretched variable,the formal asymptotic solution is constructed.And then,by using the theory of differential inequalities the uniformly validity of solution is proved.
基金supported by National Natural Science Foundation of China (Grant Nos. 11371179 and 11271172)National Science Foundation of USA (Grant No. DMS-1412454)
文摘In the one-dimensional space, traveling wave solutions of parabolic differential equations have been widely studied and well characterized. Recently, the mathematical study on higher-dimensional traveling fronts has attracted a lot of attention and many new types of nonplanar traveling waves have been observed for scalar reaction-diffusion equations with various nonlinearities. In this paper, by using the comparison argument and constructing appropriate super- and subsolutions, we study the existence, uniqueness and stability of three- dimensional traveling fronts of pyramidal shape for monotone bistable systems of reaction-diffusion equations in R3. The pyramidal traveling fronts are characterized as either a combination of planar traveling fronts on the lateral surfaces or a combination of two-dimensional V-form waves on the edges of the pyramid. In particular, our results are applicable to some important models in biology, such as Lotk,u-Volterra competition-diffusion systems with or without spatio-temporal delays, and reaction-diffusion systems of multiple obligate mutualists.
基金Supported by the Natural Science Foundation of China under Grant Nos.11371287 and 61663043
文摘On the basis of Lie group theory,(1 + N)-dimensional time-fractional partial differential equations are studied and the expression of η_α~0 is given. As applications, two special forms of nonlinear time-fractional diffusionconvection equations are investigated by Lie group analysis method. Then the equations are reduced into fractional ordinary differential equations under group transformations. Therefore, the invariant solutions and some exact solutions are obtained.
