A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems i...A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied.展开更多
A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems i...A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied.展开更多
A class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with two parameters and boundary perturbation were considered.Under suitable conditions,the existence,uniquene...A class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with two parameters and boundary perturbation were considered.Under suitable conditions,the existence,uniqueness and asymptotic behavior of solutions for the initial boundary value problems were studied.An example was also given to illustrate our main results.展开更多
A class of nonlinear singularly perturbed problems for reaction diffusion equations are considered. Under suitable conditions, by using the theory of differential inequalities, the asymptotic behavior of solutions for...A class of nonlinear singularly perturbed problems for reaction diffusion equations are considered. Under suitable conditions, by using the theory of differential inequalities, the asymptotic behavior of solutions for the initial boundary value problems are studied, reduced problems of which possess two intersecting solutions.展开更多
The singularly perturbed initial boundary value problem for a class of reaction diffusion equation is considered. Under appropriate conditions, the existence-uniqueness and the asymptotic behavior of the solution are ...The singularly perturbed initial boundary value problem for a class of reaction diffusion equation is considered. Under appropriate conditions, the existence-uniqueness and the asymptotic behavior of the solution are showed by using the fixed-point theorem.展开更多
A mathematical technique based on the consideration of a nonlinear partial differential equation together with an additional condition in the form of an ordinary differential equation is employed to study a nonlinear ...A mathematical technique based on the consideration of a nonlinear partial differential equation together with an additional condition in the form of an ordinary differential equation is employed to study a nonlinear reaction diffusion equation which describes a real process in physics and in chemistry. Several exact solutions for the equation are acquired under certain circumstances.展开更多
A class of singularly perturbed Robin problems for reaction diffusion equation is considered. Under suitable conditions the asymptotic behavior of the generalized solution for the problems are studied.
The singularly perturbed initial boundary value problem for reaction diffusion equation is considered. Under suitable conditions the existence, uniqueness and asymptotic behavior of the generalized solution for the pr...The singularly perturbed initial boundary value problem for reaction diffusion equation is considered. Under suitable conditions the existence, uniqueness and asymptotic behavior of the generalized solution for the problems are studied.展开更多
The singularly perturbed initial boundary value problems for reaction diffusion equations are considered.Under suitable conditions and by using the theory of differential inequality,the asymptotic behavior of solution...The singularly perturbed initial boundary value problems for reaction diffusion equations are considered.Under suitable conditions and by using the theory of differential inequality,the asymptotic behavior of solution for initial boundary value problems are studied,where the reduced problems possess two intersecting solutions.展开更多
In this paper we consider the initial-boundary value problems for a class ofapplications, such as biomathematics and biochemistry.Applying the method ofcomposile expansion we construct the formally asymptotic solution...In this paper we consider the initial-boundary value problems for a class ofapplications, such as biomathematics and biochemistry.Applying the method ofcomposile expansion we construct the formally asymptotic solution of the problemdescribed. With the help of theory of upper and lower solutions we prove the uniformlyvalidity of the formal solution and the existence of solution of the original problem.展开更多
In this paper, a class of nonlinear reaction diffusion singularly perturbed problem with two parameters is studied. Using the singular perturbation method, the structure of solution to the problem is discussed related...In this paper, a class of nonlinear reaction diffusion singularly perturbed problem with two parameters is studied. Using the singular perturbation method, the structure of solution to the problem is discussed related two small parameters. The asymptotic solution to the problem is given.展开更多
A class of singularly perturbed initial boundary value problems of reaction diffusion equations for nonlinear boundary conditions is considered.Under suitable conditions,by using the theory of differential inequalitie...A class of singularly perturbed initial boundary value problems of reaction diffusion equations for nonlinear boundary conditions is considered.Under suitable conditions,by using the theory of differential inequalities,the existence and asymptotic behavior of solution for initial boundary value problem are studied.Moreover,the obtained solution indicates that there are initial and boundary layers,and the thickness of the initial layer is less than that of the boundary layer.展开更多
The singularly perturbed generalized boundary value problems far the quasi- linear elliptic equation of higher order are considered. Under suitable conditions, the existence, uniqueness and asymptotic behavior of the ...The singularly perturbed generalized boundary value problems far the quasi- linear elliptic equation of higher order are considered. Under suitable conditions, the existence, uniqueness and asymptotic behavior of the generalized solution for the Dirichlet problems are studied.展开更多
1 INTRODUCTIONThe concentration distribution of reactant in porouscatalyst pellet not only is the basis of calculating theeffectiveness factor,but also has a great significancein investigating the reaction and mass tr...1 INTRODUCTIONThe concentration distribution of reactant in porouscatalyst pellet not only is the basis of calculating theeffectiveness factor,but also has a great significancein investigating the reaction and mass transfer in thecatalyst pellet.In principle,the concentration distri-bution and the effectiveness factor of a catalyst pelletcan be obtained by solving the reaction-diffusion equation.However,most of the differential equations haveno analytical solution except for some simple cases.The previous investigators have made great efforts to calculate the effectiveness factors of catalysts.They first obtained asymptotic solutions of effective-ness factor in the cases of the Thiele modulus φ→Oand φ→oo by means of perturbation method,thensynthesized the information of the asymptotic solu-展开更多
The singularly perturbed generalized boundary value problems for semi-linear elliptic equations of fourth order are considered. Under suitable conditions the existence, uniqueness and asymptotic behavior of generalize...The singularly perturbed generalized boundary value problems for semi-linear elliptic equations of fourth order are considered. Under suitable conditions the existence, uniqueness and asymptotic behavior of generalized solutions for the boundary value problems are studied.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
文摘A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied.
文摘A class of singularly perturbed initial boundary value problems for the reaction diffusion equations in a part of domain are considered. Using the operator theory the asymptotic behavior of solution for the problems is studied.
基金National Natural Science Foundation of China(No.11271372)Hunan Provincial National Natural Science Foundation of China(No.12JJ2004)the Graduate Innovation Project of Central South University,China(No.2014zzts136)
文摘A class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with two parameters and boundary perturbation were considered.Under suitable conditions,the existence,uniqueness and asymptotic behavior of solutions for the initial boundary value problems were studied.An example was also given to illustrate our main results.
基金The Importent Study Profect of the National Natural Science Poundation of China(90211004)The Natural Sciences Foundation of Zheiiang(102009)
文摘A class of nonlinear singularly perturbed problems for reaction diffusion equations are considered. Under suitable conditions, by using the theory of differential inequalities, the asymptotic behavior of solutions for the initial boundary value problems are studied, reduced problems of which possess two intersecting solutions.
基金The project is supported by the National Natural Science Foundation of China(No.10071048)
文摘The singularly perturbed initial boundary value problem for a class of reaction diffusion equation is considered. Under appropriate conditions, the existence-uniqueness and the asymptotic behavior of the solution are showed by using the fixed-point theorem.
基金supported by the Southwestern University of Finance and Economics (SWUFE) Key Subject Construction Item Funds of the 211 Project (Grant No 211D3T06)
文摘A mathematical technique based on the consideration of a nonlinear partial differential equation together with an additional condition in the form of an ordinary differential equation is employed to study a nonlinear reaction diffusion equation which describes a real process in physics and in chemistry. Several exact solutions for the equation are acquired under certain circumstances.
基金Supported by the National Natural Science Foundation of China(11371248)the Natural Science Foundation of the Education Department of Anhui Province 3(KJ2013A133,KJ2013B003)the Natural Science Foundation of Zhejiang Province(LY13A010005)
文摘A class of singularly perturbed Robin problems for reaction diffusion equation is considered. Under suitable conditions the asymptotic behavior of the generalized solution for the problems are studied.
基金Supported by the National Natural Science Foundation of China (No.90111011 and 10471039)the Natural Science Foundation of Anhui Education Office (No.2003Kj287).
文摘The singularly perturbed initial boundary value problem for reaction diffusion equation is considered. Under suitable conditions the existence, uniqueness and asymptotic behavior of the generalized solution for the problems are studied.
基金Supported by the National Natural Scince Foundation of China( 1 0 0 71 0 4 8) ,and the"Hundred TalentsProject"of Chinese Academy of Sciences
文摘The singularly perturbed initial boundary value problems for reaction diffusion equations are considered.Under suitable conditions and by using the theory of differential inequality,the asymptotic behavior of solution for initial boundary value problems are studied,where the reduced problems possess two intersecting solutions.
文摘In this paper we consider the initial-boundary value problems for a class ofapplications, such as biomathematics and biochemistry.Applying the method ofcomposile expansion we construct the formally asymptotic solution of the problemdescribed. With the help of theory of upper and lower solutions we prove the uniformlyvalidity of the formal solution and the existence of solution of the original problem.
基金Project supported by the National Natural Science Foundation of China (40676016 and40876010)the Knowledge Innovation Project of Chinese Academy of Sciences (KZCX2-YW-Q03-08)LASG State Key Laboratory Special Fund and E-Institutes of Shanghai Municipal EducationCommission (E03004)
文摘In this paper, a class of nonlinear reaction diffusion singularly perturbed problem with two parameters is studied. Using the singular perturbation method, the structure of solution to the problem is discussed related two small parameters. The asymptotic solution to the problem is given.
基金National Natural Science Foundation of China under Grant Nos.10472091,10332030 and 10502042the Natural Science Foundation of Shanxi Province under Grant No.2003A03
基金Supported by the National Natural Science Foundation of China(11071205)the Natural Science Foundation of Jiangsu Province(BK2011042)the Foundation of the Education Department of Fujian Province(JA10288)
文摘A class of singularly perturbed initial boundary value problems of reaction diffusion equations for nonlinear boundary conditions is considered.Under suitable conditions,by using the theory of differential inequalities,the existence and asymptotic behavior of solution for initial boundary value problem are studied.Moreover,the obtained solution indicates that there are initial and boundary layers,and the thickness of the initial layer is less than that of the boundary layer.
文摘The singularly perturbed generalized boundary value problems far the quasi- linear elliptic equation of higher order are considered. Under suitable conditions, the existence, uniqueness and asymptotic behavior of the generalized solution for the Dirichlet problems are studied.
基金The project supported by National Natural Science Foundation of China under Grant Nos.10371098 and 10447007the Natural Science Foundation of Shanxi Province of China under Grant No.2005A13
基金Supported by the Natural Science Foundation of Fujian Province.
文摘1 INTRODUCTIONThe concentration distribution of reactant in porouscatalyst pellet not only is the basis of calculating theeffectiveness factor,but also has a great significancein investigating the reaction and mass transfer in thecatalyst pellet.In principle,the concentration distri-bution and the effectiveness factor of a catalyst pelletcan be obtained by solving the reaction-diffusion equation.However,most of the differential equations haveno analytical solution except for some simple cases.The previous investigators have made great efforts to calculate the effectiveness factors of catalysts.They first obtained asymptotic solutions of effective-ness factor in the cases of the Thiele modulus φ→Oand φ→oo by means of perturbation method,thensynthesized the information of the asymptotic solu-
基金The Hundred People Project of Chinese Academy of Sciences.
文摘The singularly perturbed generalized boundary value problems for semi-linear elliptic equations of fourth order are considered. Under suitable conditions the existence, uniqueness and asymptotic behavior of generalized solutions for the boundary value problems are studied.
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.
