This note studies the global solutions of a semilineear reaction diffusion system which comes from an exothermic themical reaction.This is a complement of paper[1]and gives a positive answer to the question mentioned...This note studies the global solutions of a semilineear reaction diffusion system which comes from an exothermic themical reaction.This is a complement of paper[1]and gives a positive answer to the question mentioned by paper[2].展开更多
In this paper we deal with the initial boundary value problem for two classes of reaction diffusion systems with two source terms in bounded domain. Under some assumptions on the exponents and the initial data, applyi...In this paper we deal with the initial boundary value problem for two classes of reaction diffusion systems with two source terms in bounded domain. Under some assumptions on the exponents and the initial data, applying the comparison principle, the maximum prin- ciple and the supersolution-subsolution method, we prove the global existence and blow up of solutions. We also establish some upper blow up rates.展开更多
This paper deals with an initial boundary value problem for the strongly coupledreaction-diffusion systems with a full matrix of diffusion coefficients. The global existence ofsolutions is proved by using the techniqu...This paper deals with an initial boundary value problem for the strongly coupledreaction-diffusion systems with a full matrix of diffusion coefficients. The global existence ofsolutions is proved by using the techniques based on invariant regions, Lyapunov functionalmethods, and local Lp prior estimates independent of time.展开更多
A reaction diffusion system arising in the theory of superconductivity is considered and its m any kinds of analytic solutions are constructed by the Painleve′analysis and sim ilarity reduction m ethods.
The asymptotic behaviour of solutions for general partly dissipative reaction-diffusion systems in Rn is studied. The asymptotic compactness of the solutions and then the existence of the global attractor are proved i...The asymptotic behaviour of solutions for general partly dissipative reaction-diffusion systems in Rn is studied. The asymptotic compactness of the solutions and then the existence of the global attractor are proved in L2(Rn )× L2(Rn ) .展开更多
This paper is concerned with an Initial Boundary Value Problem (IBVP) for a strongly coupled semilinear reaction-diffusion system. By using the upper and lower solutions method and Leray-Schauder fixed point theorem a...This paper is concerned with an Initial Boundary Value Problem (IBVP) for a strongly coupled semilinear reaction-diffusion system. By using the upper and lower solutions method and Leray-Schauder fixed point theorem and so on, the authors prove the global existence and uniqueness of a. smooth. solution for this IBVP under some appropriate conditions.展开更多
By the degree theory on positive cone together with the technique of a priori estimate, the nontrivial equilibrium solutions of a strong nonlinearity and weak coupling reaction diffusion system and the structure of t...By the degree theory on positive cone together with the technique of a priori estimate, the nontrivial equilibrium solutions of a strong nonlinearity and weak coupling reaction diffusion system and the structure of the equilibrium solutions are discussed.展开更多
In this paper, we study properties of solutions to doubly nonlinear reaction-diffusion systems with variable density and source. We demonstrate the possibilities of the self-similar approach to studying the qualitativ...In this paper, we study properties of solutions to doubly nonlinear reaction-diffusion systems with variable density and source. We demonstrate the possibilities of the self-similar approach to studying the qualitative properties of solutions of such reaction-diffusion systems. We also study the finite speed of propagation (FSP) properties of solutions, an asymptotic behavior of the compactly supported solutions and free boundary asymptotic solutions in quick diffusive and critical cases.展开更多
In this paper,we consider nonnegative classical solutions of a Quasi-linear reaction-diffusion system with nonlinear boundary conditions.We prove the uniqueness of a nonnegative classical solution to this problem.
In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for th...In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for the corresponding problem is obtained.展开更多
The following reaction diffusion systemsare discussed, where is a bounded domain with smooth boundaryis small. Let ,where I is the unit matrix. It can be proved that solution exists globally if and only if all the pri...The following reaction diffusion systemsare discussed, where is a bounded domain with smooth boundaryis small. Let ,where I is the unit matrix. It can be proved that solution exists globally if and only if all the principal minors of A have nonnegative determinants.展开更多
Under appropriate conditions, with the perturbation method and the theory of differential inequalities, a class of weakly nonlinear singularly perturbed reaction diffusion problem is considered. The existence of solut...Under appropriate conditions, with the perturbation method and the theory of differential inequalities, a class of weakly nonlinear singularly perturbed reaction diffusion problem is considered. The existence of solution of the original problem is proved by constructing the auxiliary functions. The uniformly valid asymptotic expansions of the solution for arbitrary mth order approximation are obtained through constructing the formal solutions of the original problem, expanding the nonlinear terms to the power in small parameter ε and comparing the coefficient for the same powers of ε. Finally, an example is provided, resulting in the error of 0（ε^2）.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 problem of hydromagnetic free convection flow over a moving infinite vertical plate with Newtonian heating, mass diffusion and chemical reaction in the presence of a heat source is completely solved. Radiative and...The problem of hydromagnetic free convection flow over a moving infinite vertical plate with Newtonian heating, mass diffusion and chemical reaction in the presence of a heat source is completely solved. Radiative and porous effects are not taken into consideration but they can be immediately included by a simple rescaling of Prandtl number and magnetic parameter. Exact general solutions for the dimensionless velocity and concentration fields and the corresponding Sherwood number and skin friction coefficient are determined under integral form in terms of error function or complementary error function of Gauss. They satisfy all imposed initial and boundary conditions and can generate exact solutions for any problem with technical relevance of this type. As an interesting completion, uncommon in the literature, the differential equations which describe the thermal, concentration and momentum boundary layer, as well as the exact expressions for the thicknesses of thermal, concentration or velocity boundary layers were determined.Numerical results have shown that the thermal boundary layer thickness decreases for increasing values of Prandtl number and the concentration boundary layer thickness is decreasing with Schmidt number. Finally, for illustration,three special cases are considered and the influence of physical parameters on some fundamental motions is graphically underlined and discussed. The required time to reach the flow according with post-transient solution(the steady-state),for cosine/sine oscillating concentrations on the boundary is graphically determined. It is found that, the presence of destructive chemical reaction improves this time for increasing values of chemical reaction parameter.展开更多
This paper is concerned with the existence of traveling wave solutions in a reaction-diffusion predator-prey system with Beddington-DeAngelis functional response and a discrete time delay. By introducing a partial qua...This paper is concerned with the existence of traveling wave solutions in a reaction-diffusion predator-prey system with Beddington-DeAngelis functional response and a discrete time delay. By introducing a partial quasi-monotonicity condition and constructing a pair of upper-lower solutions, we establish the existence of traveling wave solutions. Moreover, a numerical simulation is carried out to illustrate the theoretical results.展开更多
The sediment reaction and diffusion equation,with generalized initial mid boundary condition is studied. By using Laplace transform and Jordan lemma, an analytical solution is got,,which is an extension of analytical ...The sediment reaction and diffusion equation,with generalized initial mid boundary condition is studied. By using Laplace transform and Jordan lemma, an analytical solution is got,,which is an extension of analytical solution provided by Cheng Kwokming James ( only diffusion was considered in analytical solution of Cheng). Some problems arisen in the computation of analytical solution formula are also analysed.展开更多
This paper considers the Cauchy problem of the following convection diffusion system [GRAPHICS] with initial data [GRAPHICS] A global existence result is established by employing the techniques of F. B. Weissler and t...This paper considers the Cauchy problem of the following convection diffusion system [GRAPHICS] with initial data [GRAPHICS] A global existence result is established by employing the techniques of F. B. Weissler and the energy method. Here a,b,epsilon > 0 are constants.展开更多
The generialized Kuramoto Sivashinski equation and Fisher equation in chemical reaction diffusion was studied in this paper. By introducing a new method, the anthors obtained the exact traveling wave solution for th...The generialized Kuramoto Sivashinski equation and Fisher equation in chemical reaction diffusion was studied in this paper. By introducing a new method, the anthors obtained the exact traveling wave solution for the two types of reaction diffusion equations.展开更多
文摘This note studies the global solutions of a semilineear reaction diffusion system which comes from an exothermic themical reaction.This is a complement of paper[1]and gives a positive answer to the question mentioned by paper[2].
基金supported by the National Natural Science Foundation of China(11471087)the China Postdoctoral Science Foundation(2013M540270)+1 种基金the Heilongjiang Postdoctoral Foundation(LBH-Z13056,LBHZ15036)the Fundamental Research Funds for the Central Universities
文摘In this paper we deal with the initial boundary value problem for two classes of reaction diffusion systems with two source terms in bounded domain. Under some assumptions on the exponents and the initial data, applying the comparison principle, the maximum prin- ciple and the supersolution-subsolution method, we prove the global existence and blow up of solutions. We also establish some upper blow up rates.
基金Supported by the Henan Innovation Project for University Prominent Research Talents (2003KJCX008)
文摘This paper deals with an initial boundary value problem for the strongly coupledreaction-diffusion systems with a full matrix of diffusion coefficients. The global existence ofsolutions is proved by using the techniques based on invariant regions, Lyapunov functionalmethods, and local Lp prior estimates independent of time.
文摘A reaction diffusion system arising in the theory of superconductivity is considered and its m any kinds of analytic solutions are constructed by the Painleve′analysis and sim ilarity reduction m ethods.
文摘The asymptotic behaviour of solutions for general partly dissipative reaction-diffusion systems in Rn is studied. The asymptotic compactness of the solutions and then the existence of the global attractor are proved in L2(Rn )× L2(Rn ) .
文摘This paper is concerned with an Initial Boundary Value Problem (IBVP) for a strongly coupled semilinear reaction-diffusion system. By using the upper and lower solutions method and Leray-Schauder fixed point theorem and so on, the authors prove the global existence and uniqueness of a. smooth. solution for this IBVP under some appropriate conditions.
文摘By the degree theory on positive cone together with the technique of a priori estimate, the nontrivial equilibrium solutions of a strong nonlinearity and weak coupling reaction diffusion system and the structure of the equilibrium solutions are discussed.
文摘In this paper, we study properties of solutions to doubly nonlinear reaction-diffusion systems with variable density and source. We demonstrate the possibilities of the self-similar approach to studying the qualitative properties of solutions of such reaction-diffusion systems. We also study the finite speed of propagation (FSP) properties of solutions, an asymptotic behavior of the compactly supported solutions and free boundary asymptotic solutions in quick diffusive and critical cases.
基金Supported by the National Natural Science Foundation of China(90410011)
文摘In this paper,we consider nonnegative classical solutions of a Quasi-linear reaction-diffusion system with nonlinear boundary conditions.We prove the uniqueness of a nonnegative classical solution to this problem.
基金Supported by the National Natural Sciences Foundation of China(40676016 and 10471039)the National Key Project for Basic Research(2003CB415101-03 and 2004CB418304)+2 种基金the Key Project of the Chinese Academy of Sciences(KZCX3-SW-221)in part by E-Institutes of Shanghai Municipal Education Commission(N.E03004)the Natural Science Foundation of Zeijiang,China(Y606268).
文摘In this article the travelling wave solution for a class of nonlinear reaction diffusion problems are considered. Using the homotopic method and the theory of travelling wave transform, the approximate solution for the corresponding problem is obtained.
基金Project supported by the National Natural Science Foundation of Chinathe Natural Science Foundation of Jiangsu Province.
文摘The following reaction diffusion systemsare discussed, where is a bounded domain with smooth boundaryis small. Let ,where I is the unit matrix. It can be proved that solution exists globally if and only if all the principal minors of A have nonnegative determinants.
基金supported by the E-Institutes of Shanghai Municipal Education Commission (Grant No.E03004)
文摘Under appropriate conditions, with the perturbation method and the theory of differential inequalities, a class of weakly nonlinear singularly perturbed reaction diffusion problem is considered. The existence of solution of the original problem is proved by constructing the auxiliary functions. The uniformly valid asymptotic expansions of the solution for arbitrary mth order approximation are obtained through constructing the formal solutions of the original problem, expanding the nonlinear terms to the power in small parameter ε and comparing the coefficient for the same powers of ε. Finally, an example is provided, resulting in the error of 0（ε^2）.
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Abdus Salam School of Mathematical Sciences, GC University, Lahore, PakistanHigher Education Commission of Pakistan, for generous supporting and facilitating this research work
文摘The problem of hydromagnetic free convection flow over a moving infinite vertical plate with Newtonian heating, mass diffusion and chemical reaction in the presence of a heat source is completely solved. Radiative and porous effects are not taken into consideration but they can be immediately included by a simple rescaling of Prandtl number and magnetic parameter. Exact general solutions for the dimensionless velocity and concentration fields and the corresponding Sherwood number and skin friction coefficient are determined under integral form in terms of error function or complementary error function of Gauss. They satisfy all imposed initial and boundary conditions and can generate exact solutions for any problem with technical relevance of this type. As an interesting completion, uncommon in the literature, the differential equations which describe the thermal, concentration and momentum boundary layer, as well as the exact expressions for the thicknesses of thermal, concentration or velocity boundary layers were determined.Numerical results have shown that the thermal boundary layer thickness decreases for increasing values of Prandtl number and the concentration boundary layer thickness is decreasing with Schmidt number. Finally, for illustration,three special cases are considered and the influence of physical parameters on some fundamental motions is graphically underlined and discussed. The required time to reach the flow according with post-transient solution(the steady-state),for cosine/sine oscillating concentrations on the boundary is graphically determined. It is found that, the presence of destructive chemical reaction improves this time for increasing values of chemical reaction parameter.
文摘This paper is concerned with the existence of traveling wave solutions in a reaction-diffusion predator-prey system with Beddington-DeAngelis functional response and a discrete time delay. By introducing a partial quasi-monotonicity condition and constructing a pair of upper-lower solutions, we establish the existence of traveling wave solutions. Moreover, a numerical simulation is carried out to illustrate the theoretical results.
文摘The sediment reaction and diffusion equation,with generalized initial mid boundary condition is studied. By using Laplace transform and Jordan lemma, an analytical solution is got,,which is an extension of analytical solution provided by Cheng Kwokming James ( only diffusion was considered in analytical solution of Cheng). Some problems arisen in the computation of analytical solution formula are also analysed.
文摘This paper considers the Cauchy problem of the following convection diffusion system [GRAPHICS] with initial data [GRAPHICS] A global existence result is established by employing the techniques of F. B. Weissler and the energy method. Here a,b,epsilon > 0 are constants.
文摘The generialized Kuramoto Sivashinski equation and Fisher equation in chemical reaction diffusion was studied in this paper. By introducing a new method, the anthors obtained the exact traveling wave solution for the two types of reaction diffusion equations.
