By means of a nonstandard estimation about the energy functional, the authors prove the existence of a global attractor for an abstract nonlinear evolution equation. As an application, the existence of a global attrac...By means of a nonstandard estimation about the energy functional, the authors prove the existence of a global attractor for an abstract nonlinear evolution equation. As an application, the existence of a global attractor for some nonlinear reaction-diffusion equations with some distribution derivatives in inhomogeneous terms is obtained.展开更多
The integer-order interdependent calcium([Ca^(2+)])and nitric oxide(NO)systems are unable to shed light on the influences of the superdiffusion and memory in triggering Brownian motion(BM)in neurons.Therefore,a mathem...The integer-order interdependent calcium([Ca^(2+)])and nitric oxide(NO)systems are unable to shed light on the influences of the superdiffusion and memory in triggering Brownian motion(BM)in neurons.Therefore,a mathematical model is constructed for the fractional-order nonlinear spatiotemporal systems of[Ca^(2+)]and NO incorporating reaction-diffusion equations in neurons.The two-way feedback process between[Ca^(2+)]and NO systems through calcium feedback on NO production and NO feedback on calcium through cyclic guanosine monophosphate(cGMP)with plasmalemmal[Ca^(2+)]-ATPase(PMCA)was incorporated in the model.The Crank–Nicholson scheme(CNS)with Grunwald approximation along spatial derivatives and L1 scheme along temporal derivatives with Gauss–Seidel(GS)iterations were employed.The numerical outcomes were analyzed to get insights into superdiffusion,buffer,and memory exhibiting BM of[Ca^(2+)]and NO systems.The conditions,events and mechanisms leading to dysfunctions in calcium and NO systems and causing different diseases like Parkinson’s were explored in neurons.展开更多
When hyperthermal atomic oxygen collides with a silicon surface, an ultrathin oxidation regime characterized by fractional atomic-oxygen anions having low diffusive and reactive barriers, along with their enhanced dif...When hyperthermal atomic oxygen collides with a silicon surface, an ultrathin oxidation regime characterized by fractional atomic-oxygen anions having low diffusive and reactive barriers, along with their enhanced diffusion due to both the electric field and image potential, will form on the surface. In ac- cordance with these properties, an attempt was made in the present study to modify the Almeida- Goncalves-Baumvol (AGB) model by setting the diffusivity and reaction rate constant to be diffu- sion-length dependence. According to the modified model, numerical parametric studies for oxidation thin growth were performed. The dependencies of the diffusion coefficient, the reaction rate constant, the attenuation length, and the adjustable parameter upon the translational kinetic energy, flux, tem- perature, and tangential flux of atomic oxygen were analyzed briefly via the fitting of the experimental data given by Tagawa et al. The numerical results confirmed the rationality of the modified diffu- sion-reaction model. The model together with the computer code developed in this study would be a useful tool for thickness evaluation of the protective film against the oxidation of atomic oxygen toward spacecraft surface materials in LEO environment.展开更多
The initial boundary value problem of wave equations and reaction-diffusion equations with several nonlinear source terms in a bounded domain is studied by potential well method. The invarianee of some sets under the ...The initial boundary value problem of wave equations and reaction-diffusion equations with several nonlinear source terms in a bounded domain is studied by potential well method. The invarianee of some sets under the flow of these problems and the vacuum isolation of solutions are obtained by introducing a family of potential wells. Then the threshold result of global existence and nonexistence of solutions are given. Finally, the problem with critical initial conditions are discussed.展开更多
Based on the computerized symbolic,a new generalized tanh functions method is used for constructing exact travelling wave solutions of nonlinear partial differential equations (PDES)in a unified way.The main idea of o...Based on the computerized symbolic,a new generalized tanh functions method is used for constructing exact travelling wave solutions of nonlinear partial differential equations (PDES)in a unified way.The main idea of our method is to take full advantage of an auxiliary ordinary differential equation which has more new solutions.At the same time,we present a more general transformation,which is a generalized method for finding more types of travelling wave solutions of nonlinear evolution equations(NLEEs).More new exact travelling wave solutions to two nonlinear systems are explicitly obtained.展开更多
Singular limit is investigated for reaction-diffusion equations with an additive noise in a bounded domain of R^2. The solution converges to one of the two stable phases {+1, -1} determined from the reaction term; acc...Singular limit is investigated for reaction-diffusion equations with an additive noise in a bounded domain of R^2. The solution converges to one of the two stable phases {+1, -1} determined from the reaction term; accordingly a phase separation curve is generated in the limit. We shall derive a randomly perturbed motion by curvature for the dynamics of the phase separation curve.展开更多
This paper studies the multidimensional stability of traveling fronts in monostable reaction-difusion equations,including Ginzburg-Landau equations and Fisher-KPP equations.Eckmann and Wayne(1994)showed a one-dimensio...This paper studies the multidimensional stability of traveling fronts in monostable reaction-difusion equations,including Ginzburg-Landau equations and Fisher-KPP equations.Eckmann and Wayne(1994)showed a one-dimensional stability result of traveling fronts with speeds c c(the critical speed)under complex perturbations.In the present work,we prove that these traveling fronts are also asymptotically stable subject to complex perturbations in multiple space dimensions(n=2,3),employing weighted energy methods.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 19971036)the Trans-Century Training Programme Foundation for the Talents by the Ministry of Education of China.
文摘By means of a nonstandard estimation about the energy functional, the authors prove the existence of a global attractor for an abstract nonlinear evolution equation. As an application, the existence of a global attractor for some nonlinear reaction-diffusion equations with some distribution derivatives in inhomogeneous terms is obtained.
文摘The integer-order interdependent calcium([Ca^(2+)])and nitric oxide(NO)systems are unable to shed light on the influences of the superdiffusion and memory in triggering Brownian motion(BM)in neurons.Therefore,a mathematical model is constructed for the fractional-order nonlinear spatiotemporal systems of[Ca^(2+)]and NO incorporating reaction-diffusion equations in neurons.The two-way feedback process between[Ca^(2+)]and NO systems through calcium feedback on NO production and NO feedback on calcium through cyclic guanosine monophosphate(cGMP)with plasmalemmal[Ca^(2+)]-ATPase(PMCA)was incorporated in the model.The Crank–Nicholson scheme(CNS)with Grunwald approximation along spatial derivatives and L1 scheme along temporal derivatives with Gauss–Seidel(GS)iterations were employed.The numerical outcomes were analyzed to get insights into superdiffusion,buffer,and memory exhibiting BM of[Ca^(2+)]and NO systems.The conditions,events and mechanisms leading to dysfunctions in calcium and NO systems and causing different diseases like Parkinson’s were explored in neurons.
基金Supported by the National Natural Science Foundation of China (Grant No. 10572016)
文摘When hyperthermal atomic oxygen collides with a silicon surface, an ultrathin oxidation regime characterized by fractional atomic-oxygen anions having low diffusive and reactive barriers, along with their enhanced diffusion due to both the electric field and image potential, will form on the surface. In ac- cordance with these properties, an attempt was made in the present study to modify the Almeida- Goncalves-Baumvol (AGB) model by setting the diffusivity and reaction rate constant to be diffu- sion-length dependence. According to the modified model, numerical parametric studies for oxidation thin growth were performed. The dependencies of the diffusion coefficient, the reaction rate constant, the attenuation length, and the adjustable parameter upon the translational kinetic energy, flux, tem- perature, and tangential flux of atomic oxygen were analyzed briefly via the fitting of the experimental data given by Tagawa et al. The numerical results confirmed the rationality of the modified diffu- sion-reaction model. The model together with the computer code developed in this study would be a useful tool for thickness evaluation of the protective film against the oxidation of atomic oxygen toward spacecraft surface materials in LEO environment.
基金the National Natural Science Foundation of China(No.10271034)the Basic Research Foundation of Harbin Engineering University(No.HEUF04012)
文摘The initial boundary value problem of wave equations and reaction-diffusion equations with several nonlinear source terms in a bounded domain is studied by potential well method. The invarianee of some sets under the flow of these problems and the vacuum isolation of solutions are obtained by introducing a family of potential wells. Then the threshold result of global existence and nonexistence of solutions are given. Finally, the problem with critical initial conditions are discussed.
文摘Based on the computerized symbolic,a new generalized tanh functions method is used for constructing exact travelling wave solutions of nonlinear partial differential equations (PDES)in a unified way.The main idea of our method is to take full advantage of an auxiliary ordinary differential equation which has more new solutions.At the same time,we present a more general transformation,which is a generalized method for finding more types of travelling wave solutions of nonlinear evolution equations(NLEEs).More new exact travelling wave solutions to two nonlinear systems are explicitly obtained.
文摘Singular limit is investigated for reaction-diffusion equations with an additive noise in a bounded domain of R^2. The solution converges to one of the two stable phases {+1, -1} determined from the reaction term; accordingly a phase separation curve is generated in the limit. We shall derive a randomly perturbed motion by curvature for the dynamics of the phase separation curve.
基金supported by National Science Foundation of USA(Grant No.DMS-0818717)
文摘This paper studies the multidimensional stability of traveling fronts in monostable reaction-difusion equations,including Ginzburg-Landau equations and Fisher-KPP equations.Eckmann and Wayne(1994)showed a one-dimensional stability result of traveling fronts with speeds c c(the critical speed)under complex perturbations.In the present work,we prove that these traveling fronts are also asymptotically stable subject to complex perturbations in multiple space dimensions(n=2,3),employing weighted energy methods.
基金Supported by the Special Funds for Major Specialities of Shanghai Education Committee(No.00JC14057)Shanghai Development Foundation for Science and Technology(No.03QA14036).
