A class of nonlinear differential-integral singular perturbation problem for the disturbed evolution equations is studied. Using the singular perturbation method, the structure of solution to problem is discussed in t...A class of nonlinear differential-integral singular perturbation problem for the disturbed evolution equations is studied. Using the singular perturbation method, the structure of solution to problem is discussed in the cases of two small parameters and under the suitable conditions. Firstly, the outer solution to boundary value problem is given. Secondly, constructing the non-singular coordinate system near the boundary, the variables of multiple scales is introduced to obtain the boundary layer corrective term for the solution. Then the stretched variable is applied to get the initial layer correction term. Finally, using the fix point theorem, the uniformly valid asymptotic expansion of the solution to problem is proved. The proposed method possesses the advantages of convenient use and high accuracy.展开更多
Both the inplane and out-of-plane transverse vibrations of aviscoelastic cable subjected to an initial stress distributinguniform on the cross section are studied. The constitution of thecable material is as- sumed to...Both the inplane and out-of-plane transverse vibrations of aviscoelastic cable subjected to an initial stress distributinguniform on the cross section are studied. The constitution of thecable material is as- sumed to be of the hereditary integral type.The partial differential -integral equations of motion are derivedfirst. Then by applying Galerkin's method, the governing equationsare reduced to a set of second-order non- linear differential-integral equations which are solved by finite difference numericalintegration procedures. Finally, the effects of the viscosityparameter and the elastic parameter on the transient amplitudes ofthe first Mode are investigated by numerical simulation.展开更多
Predictive modeling of the evolutionary dynamics of cancer is a challenging issue in computational cancer biology.In this paper,we propose a general mathematical model framework for the evolutionary dynamics of cancer...Predictive modeling of the evolutionary dynamics of cancer is a challenging issue in computational cancer biology.In this paper,we propose a general mathematical model framework for the evolutionary dynamics of cancer,including plasticity and heterogeneity in cancer cells.Cancer is a group of diseases involving abnormal cell growth,during which abnormal regulation of stem cell regeneration is essential for the dynamics of cancer development.In general,the dynamics of stem cell regeneration can be simplified as a G0 phase cell cycle model,which leads to a delay differentiation equation.When cell heterogeneity and plasticity are considered,we establish a differential-integral equation based on the random transition of epigenetic states of stem cells during cell division.The proposed model highlights cell heterogeneity and plasticity;connects the heterogeneity with cell-to-cell variance in cellular behaviors(for example,proliferation,apoptosis,and differentiation/senescence);and can be extended to include gene mutation-induced tumor development.Hybrid computational models are developed based on the mathematical model framework and are applied to the processes of inflammationinduced tumorigenesis and tumor relapse after chimeric antigen receptor(CAR)-T cell therapy.Finally,we propose several mathematical problems related to the proposed differential-integral equation.Solutions to these problems are crucial for understanding the evolutionary dynamics of cancer.展开更多
Some new generalized retarded nonlinear integral inequalities are discussed and upper bound estimations of unknown functions are given by adapting novel analysis techniques. These estimations can be applied to study d...Some new generalized retarded nonlinear integral inequalities are discussed and upper bound estimations of unknown functions are given by adapting novel analysis techniques. These estimations can be applied to study differential-integral equations and some practical problems in engineering.展开更多
基金Supported by the National Natural Science Foundation of China(11202106)the Natural Science Foundation of the Education Department of Anhui Province(KJ2017A702)the Key Projects of Outstanding Young Talents of Universities in Anhui Province(gxyqZD2016520)
文摘A class of nonlinear differential-integral singular perturbation problem for the disturbed evolution equations is studied. Using the singular perturbation method, the structure of solution to problem is discussed in the cases of two small parameters and under the suitable conditions. Firstly, the outer solution to boundary value problem is given. Secondly, constructing the non-singular coordinate system near the boundary, the variables of multiple scales is introduced to obtain the boundary layer corrective term for the solution. Then the stretched variable is applied to get the initial layer correction term. Finally, using the fix point theorem, the uniformly valid asymptotic expansion of the solution to problem is proved. The proposed method possesses the advantages of convenient use and high accuracy.
基金the National Natural Science Foundation of China (No.59635140)the National Postdoctoral Foundation of China.
文摘Both the inplane and out-of-plane transverse vibrations of aviscoelastic cable subjected to an initial stress distributinguniform on the cross section are studied. The constitution of thecable material is as- sumed to be of the hereditary integral type.The partial differential -integral equations of motion are derivedfirst. Then by applying Galerkin's method, the governing equationsare reduced to a set of second-order non- linear differential-integral equations which are solved by finite difference numericalintegration procedures. Finally, the effects of the viscosityparameter and the elastic parameter on the transient amplitudes ofthe first Mode are investigated by numerical simulation.
基金supported by National Natural Science Foundation of China(Grant Nos.91730101 and 11831015)
文摘Predictive modeling of the evolutionary dynamics of cancer is a challenging issue in computational cancer biology.In this paper,we propose a general mathematical model framework for the evolutionary dynamics of cancer,including plasticity and heterogeneity in cancer cells.Cancer is a group of diseases involving abnormal cell growth,during which abnormal regulation of stem cell regeneration is essential for the dynamics of cancer development.In general,the dynamics of stem cell regeneration can be simplified as a G0 phase cell cycle model,which leads to a delay differentiation equation.When cell heterogeneity and plasticity are considered,we establish a differential-integral equation based on the random transition of epigenetic states of stem cells during cell division.The proposed model highlights cell heterogeneity and plasticity;connects the heterogeneity with cell-to-cell variance in cellular behaviors(for example,proliferation,apoptosis,and differentiation/senescence);and can be extended to include gene mutation-induced tumor development.Hybrid computational models are developed based on the mathematical model framework and are applied to the processes of inflammationinduced tumorigenesis and tumor relapse after chimeric antigen receptor(CAR)-T cell therapy.Finally,we propose several mathematical problems related to the proposed differential-integral equation.Solutions to these problems are crucial for understanding the evolutionary dynamics of cancer.
基金supported by the NNSF of China(Grants 11171178 and 11271225)program for scientific research innovation team in colleges and universities of Shandong Province,scientific research training project for talent students(201310446008)
文摘Some new generalized retarded nonlinear integral inequalities are discussed and upper bound estimations of unknown functions are given by adapting novel analysis techniques. These estimations can be applied to study differential-integral equations and some practical problems in engineering.
