Asymptotical properties for the solutions of neutral parabolic systems with Robin boundary conditions were analyzed by using the inequality analysis.The oscillations problems for the neutral parabolic systems were con...Asymptotical properties for the solutions of neutral parabolic systems with Robin boundary conditions were analyzed by using the inequality analysis.The oscillations problems for the neutral parabolic systems were considered and some oscillation criteria for the systems were established.展开更多
In this paper, the estimate on blow-up rate of the following nonlinear parabolic system is considered：{ut=uxx＋u^l 11v^l 12,vt=vxx＋u^l21v^l22,（x,t）∈（0,1）×（0,T）,ux（0,t）=0,vx（0,t）=0,t∈（0,T）,ux（1,t...In this paper, the estimate on blow-up rate of the following nonlinear parabolic system is considered：{ut=uxx＋u^l 11v^l 12,vt=vxx＋u^l21v^l22,（x,t）∈（0,1）×（0,T）,ux（0,t）=0,vx（0,t）=0,t∈（0,T）,ux（1,t）=（u^p11v^p12）（1,t）,vx（1,t）=（u^p21v^p22）（1,t）,t∈（0,T）,u（x,0）=u0（x）,v（x,0）=v0（x）,x∈（0,1）We will prove that there exist two positive constants such that：c≤max x∈[0,1]u（x,t）（T-t）^r（l1-1）≤C,0〈t〈T,c≤max x∈[0,1] v（x,t）（T-t）^1/（t1-1）≤C,0〈t〈T.where l1=l21α/α2＋l22,r=α1/α2〉1,α1≤α2〈0.展开更多
This paper deals with the existence and nonexistence of global positive solution of the following equation:where p, q, m, α are parameters with is a bounded domain with Ω smooth enough, The necessary and sufficient ...This paper deals with the existence and nonexistence of global positive solution of the following equation:where p, q, m, α are parameters with is a bounded domain with Ω smooth enough, The necessary and sufficient conditions for the global existence of solution are obtained.展开更多
In this paper the author constructs a solution of parabolic stochastic partial differential equation with random initial conditions by Kolmogorov's criterion.
Abstract. In this paper, we discuss the limit behaviour of solutious to equivalued surfaceboundary value problem for parabolic equations when the equivalued surface boundaryshrinks to a point and the space dimension o...Abstract. In this paper, we discuss the limit behaviour of solutious to equivalued surfaceboundary value problem for parabolic equations when the equivalued surface boundaryshrinks to a point and the space dimension of the domain is two or more.展开更多
The initial-Dirichlet and initial-Neumann problems in Lipschitz cylinders are studied forthe general second order parabolic equations of constant coefficients with squarely integrableboundary data. By layer potential ...The initial-Dirichlet and initial-Neumann problems in Lipschitz cylinders are studied forthe general second order parabolic equations of constant coefficients with squarely integrableboundary data. By layer potential method developed in the past decade, the author provesthat the double layer potential and the single layer potential operators are invertible and henceobtains the solvability of the initial boundsry value problems. Also, the solutions can berepresented by these operators.展开更多
In this paper, we investigate the existence, stability and global attractivity of T-periodic solutions for a class of quasilinear parabolic equations under Robin boundary conditions. We obtain that periodic solutions ...In this paper, we investigate the existence, stability and global attractivity of T-periodic solutions for a class of quasilinear parabolic equations under Robin boundary conditions. We obtain that periodic solutions exist if the inter-specific competition rates are weak. The numerical simulations are also presented to illustrate our result.展开更多
This paper is concerned with a system of semilinear parabolic equations with two free boundaries describing the spreading fronts of the invasive species in a mutualistic eco- logical model. The local existence and uni...This paper is concerned with a system of semilinear parabolic equations with two free boundaries describing the spreading fronts of the invasive species in a mutualistic eco- logical model. The local existence and uniqueness of a classical solution are obtained and the asymptotic behavior of the free boundary problem is studied. Our results indi- cate that two free boundaries tend monotonically to finite or infinite limits at the same time, and the free boundary problem admits a global slow solution with unbounded free boundaries if the intra-specific competitions are strong, while if the intra-specific competitions are weak, there exist the blowup solution and global fast solution.展开更多
文摘Asymptotical properties for the solutions of neutral parabolic systems with Robin boundary conditions were analyzed by using the inequality analysis.The oscillations problems for the neutral parabolic systems were considered and some oscillation criteria for the systems were established.
文摘In this paper, the estimate on blow-up rate of the following nonlinear parabolic system is considered：{ut=uxx＋u^l 11v^l 12,vt=vxx＋u^l21v^l22,（x,t）∈（0,1）×（0,T）,ux（0,t）=0,vx（0,t）=0,t∈（0,T）,ux（1,t）=（u^p11v^p12）（1,t）,vx（1,t）=（u^p21v^p22）（1,t）,t∈（0,T）,u（x,0）=u0（x）,v（x,0）=v0（x）,x∈（0,1）We will prove that there exist two positive constants such that：c≤max x∈[0,1]u（x,t）（T-t）^r（l1-1）≤C,0〈t〈T,c≤max x∈[0,1] v（x,t）（T-t）^1/（t1-1）≤C,0〈t〈T.where l1=l21α/α2＋l22,r=α1/α2〉1,α1≤α2〈0.
文摘This paper deals with the existence and nonexistence of global positive solution of the following equation:where p, q, m, α are parameters with is a bounded domain with Ω smooth enough, The necessary and sufficient conditions for the global existence of solution are obtained.
基金Project supported by the National Natural Science Foundation of China (No.10301011)the 973 Project of the Ministry of Science and Technology of China.
文摘In this paper the author constructs a solution of parabolic stochastic partial differential equation with random initial conditions by Kolmogorov's criterion.
基金NSF of Shandong Province (No.Y98A09012, No. Q99A05.)
文摘Abstract. In this paper, we discuss the limit behaviour of solutious to equivalued surfaceboundary value problem for parabolic equations when the equivalued surface boundaryshrinks to a point and the space dimension of the domain is two or more.
文摘The initial-Dirichlet and initial-Neumann problems in Lipschitz cylinders are studied forthe general second order parabolic equations of constant coefficients with squarely integrableboundary data. By layer potential method developed in the past decade, the author provesthat the double layer potential and the single layer potential operators are invertible and henceobtains the solvability of the initial boundsry value problems. Also, the solutions can berepresented by these operators.
文摘In this paper, we investigate the existence, stability and global attractivity of T-periodic solutions for a class of quasilinear parabolic equations under Robin boundary conditions. We obtain that periodic solutions exist if the inter-specific competition rates are weak. The numerical simulations are also presented to illustrate our result.
文摘This paper is concerned with a system of semilinear parabolic equations with two free boundaries describing the spreading fronts of the invasive species in a mutualistic eco- logical model. The local existence and uniqueness of a classical solution are obtained and the asymptotic behavior of the free boundary problem is studied. Our results indi- cate that two free boundaries tend monotonically to finite or infinite limits at the same time, and the free boundary problem admits a global slow solution with unbounded free boundaries if the intra-specific competitions are strong, while if the intra-specific competitions are weak, there exist the blowup solution and global fast solution.
