A class of initial boundary value problems for the reaction diffusion equations are considered.The asymptotic behavior of solution for the problem is obtained using the theory of differential inequality.
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
We study the Cauchy problem for nonlocal reaction diffusion equations with bistable nonlinearity in 1D spatial domain and investigate the asymptotic behaviors of solutions with a one-parameter family of monotonically ...We study the Cauchy problem for nonlocal reaction diffusion equations with bistable nonlinearity in 1D spatial domain and investigate the asymptotic behaviors of solutions with a one-parameter family of monotonically increasing and compactly supported initial data.We show that for small values of the parameter the corresponding solutions decay to O,while for large values the related solutions converge to 1 uniformly on compacts.Moreover,we prove that the transition from extinction(converging to O)to propagation(converging to 1)is sharp.Numerical results are provided to verify the theoretical results.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
In this paper the nonlinear reaction diffusion problems with ultraparabolic equations are considered. By using comparison theorem, the existence, uniqueness and asymptotic behavior of solution for the problem are stud...In this paper the nonlinear reaction diffusion problems with ultraparabolic equations are considered. By using comparison theorem, the existence, uniqueness and asymptotic behavior of solution for the problem are studied.展开更多
The asymptotic behavior and oscillation of the solutions of second order integro-differential equations with deviating argumentis studied. Our technique depends on an integral inequality containing a deviating argumen...The asymptotic behavior and oscillation of the solutions of second order integro-differential equations with deviating argumentis studied. Our technique depends on an integral inequality containing a deviating argument. From this we obtain some sufficient conditions under which all solutions of Eq.(1.4) have some asymptotic behavior and oscillation.展开更多
In this paper,we study the asymptotic behavior of solutions to a class of higher order nonlinear integro-differential equations with deviating arguments. And some properties of the oscillatory solutions are given. Our...In this paper,we study the asymptotic behavior of solutions to a class of higher order nonlinear integro-differential equations with deviating arguments. And some properties of the oscillatory solutions are given. Our results generalize and improve the previous results.展开更多
In this paper, we first consider a delay difference equation of neutral type of the form: Δ(y_n+py_(n-k))+q_ny_(n-)=0 for n∈Z^+(0) (1*) and give a different condition from that of Yu and Wang (Funkcial Ekvac, 1994,...In this paper, we first consider a delay difference equation of neutral type of the form: Δ(y_n+py_(n-k))+q_ny_(n-)=0 for n∈Z^+(0) (1*) and give a different condition from that of Yu and Wang (Funkcial Ekvac, 1994, 37(2): 241 248) to guarantee that every non-oscillatory solution of (1~*) with p=1 tends to zero as n→∞ Moreover, we consider a delay reaction-diffusion difference equation of neutral type of the form: Δ_1(u_(n,m)+pu_(n-k,m)+q_(n,m)u_(n-m)=a^2Δ_2~2u_(n+1,m-1) for (n,m)∈Z^+(0)×Ω. (2*) study various casks of p in the neutral term and obtain that if p≥-1 then every non-oscillatory solution of (2~*) tends uniformly in m∈Ω to zero as n→∞: if p=-1 then every solution of (2~*) oscillates and if p<-1 then every non-oscillatory solution of (2~*) goes uniformly in m∈Ω to infinity or minus infinity as n→∞ under some hypotheses.展开更多
基金the National Natural Science Foundation of China( 90 2 1 1 0 0 4 ,1 0 4 71 0 39) ,and by the"Hundred Talents Project"of Chinese Academy of Sciences
文摘A class of initial boundary value problems for the reaction diffusion equations are considered.The asymptotic behavior of solution for the problem is obtained using the theory of differential inequality.
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supported in part by NSFC(Grant Nos.12071175,11171132,11571065)National Research Program of China(Grant No.2013CB834100)+1 种基金by the Natural Science Foundation of jilin Province(Grant Nos.20200201253JC,201902013020JC)by the Project of Science and Technology Development of Jilin Province,China(Grant No.2017C028-1).
文摘We study the Cauchy problem for nonlocal reaction diffusion equations with bistable nonlinearity in 1D spatial domain and investigate the asymptotic behaviors of solutions with a one-parameter family of monotonically increasing and compactly supported initial data.We show that for small values of the parameter the corresponding solutions decay to O,while for large values the related solutions converge to 1 uniformly on compacts.Moreover,we prove that the transition from extinction(converging to O)to propagation(converging to 1)is sharp.Numerical results are provided to verify the theoretical results.
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 NNSF of China(40676016,10471039)the National Key Project for Basics Research(2003CB415101-03 and 2004CB418304)+1 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).
文摘In this paper the nonlinear reaction diffusion problems with ultraparabolic equations are considered. By using comparison theorem, the existence, uniqueness and asymptotic behavior of solution for the problem are studied.
文摘The asymptotic behavior and oscillation of the solutions of second order integro-differential equations with deviating argumentis studied. Our technique depends on an integral inequality containing a deviating argument. From this we obtain some sufficient conditions under which all solutions of Eq.(1.4) have some asymptotic behavior and oscillation.
文摘In this paper,we study the asymptotic behavior of solutions to a class of higher order nonlinear integro-differential equations with deviating arguments. And some properties of the oscillatory solutions are given. Our results generalize and improve the previous results.
基金Research supported by Youth Science Foundation of Naval Aeronautical Engineering AcademyNational Natural Science Foundation of China (# 69974032).
文摘In this paper, we first consider a delay difference equation of neutral type of the form: Δ(y_n+py_(n-k))+q_ny_(n-)=0 for n∈Z^+(0) (1*) and give a different condition from that of Yu and Wang (Funkcial Ekvac, 1994, 37(2): 241 248) to guarantee that every non-oscillatory solution of (1~*) with p=1 tends to zero as n→∞ Moreover, we consider a delay reaction-diffusion difference equation of neutral type of the form: Δ_1(u_(n,m)+pu_(n-k,m)+q_(n,m)u_(n-m)=a^2Δ_2~2u_(n+1,m-1) for (n,m)∈Z^+(0)×Ω. (2*) study various casks of p in the neutral term and obtain that if p≥-1 then every non-oscillatory solution of (2~*) tends uniformly in m∈Ω to zero as n→∞: if p=-1 then every solution of (2~*) oscillates and if p<-1 then every non-oscillatory solution of (2~*) goes uniformly in m∈Ω to infinity or minus infinity as n→∞ under some hypotheses.
基金Supported by the NNSF of China(90111011,10471039)the National Key Project for Basics Re-search(2003CB415101-03,2004CB418304)the Key Project of the Chinese Academy of Sciences(KZCX3-SW-221)and in part by E-Institutes of Shanghai Municipal Education Commission(N.E03004)
基金Supported by the NSFC(No．40676016，10471039)the National Key Project for Basics Research(No．2003CB415101-03 and No．2004CB418304)+1 种基金the Key Project of the Chinese Academy of Sciences(No．KZCX3-SW-221)in part by E-Institutes of Shanghai Municipal Education Commission(No．E03004)．
