The Dirichlet initial-boundary value problem of a compressible reactive gas model equation with a nonlocal nonlinear source term is investigated. Under certain conditions, it can be proven that the blow-up rate is uni...The Dirichlet initial-boundary value problem of a compressible reactive gas model equation with a nonlocal nonlinear source term is investigated. Under certain conditions, it can be proven that the blow-up rate is uniform in all compact subsets of the domain, and the blow-up rate is irrelative to the exponent of the diffusion term, however, relative to the exponent of the nonlocal nonlinear source.展开更多
The nonlocal singularly perturbed nonlinear problem is considered. Underthe appropriate assumptions the author proved that there exists a solution andthe estimation of solution is obtained using the method of differe...The nonlocal singularly perturbed nonlinear problem is considered. Underthe appropriate assumptions the author proved that there exists a solution andthe estimation of solution is obtained using the method of differential inequalities and a class of boundary layer functions.展开更多
In this paper, we study a fractional differential equation cD0^a＋u（t）＋f（t,u（t））=0,t∈（0＋∞）satisfying the boundary conditions： ……where 1〈a≤2,cD0^a＋ is the standard Caputo fractional derivative of orde...In this paper, we study a fractional differential equation cD0^a＋u（t）＋f（t,u（t））=0,t∈（0＋∞）satisfying the boundary conditions： ……where 1〈a≤2,cD0^a＋ is the standard Caputo fractional derivative of order a. The main tools used in the paper is a contraction principle in the Banach space and the fixed point theorem due to D. O＇Regan. Under a compactness criterion, the existence of solutions are established.展开更多
考虑了非局部边值问题{-a(∫Ω|u|qdx)Δu+b(l(u))u=f(x,u), in Ω,u=0, on Ω,及其相应的非局部抛物问题的正解存在性.其中Ω是RN中的有界光滑区域,a和b是给定的函数.利用Galerkin方法,首先获得了具有低阶项的非局部椭圆问题正解的...考虑了非局部边值问题{-a(∫Ω|u|qdx)Δu+b(l(u))u=f(x,u), in Ω,u=0, on Ω,及其相应的非局部抛物问题的正解存在性.其中Ω是RN中的有界光滑区域,a和b是给定的函数.利用Galerkin方法,首先获得了具有低阶项的非局部椭圆问题正解的存在性,进一步证明了抛物问题正解的存在性.展开更多
The nonlocal theory which confiders interatomic long-range interaction in materials is one of the generalized continuum theories which involve the microstructure characteristic of material media. The basic equations o...The nonlocal theory which confiders interatomic long-range interaction in materials is one of the generalized continuum theories which involve the microstructure characteristic of material media. The basic equations of linear, homogeneous, isotropic, nonlocal elastic solids展开更多
基金supported by the National Natural Science Foundation of China (No. 11101102)the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20102304120022)+2 种基金the Natural Science Foundation of Heilongjiang Province of China (No. A201014)the Foundational Science Foundation of Harbin Engineering Universitythe Fundamental Research Funds for the Central Universities (No. HEUCF20111101)
文摘The Dirichlet initial-boundary value problem of a compressible reactive gas model equation with a nonlocal nonlinear source term is investigated. Under certain conditions, it can be proven that the blow-up rate is uniform in all compact subsets of the domain, and the blow-up rate is irrelative to the exponent of the diffusion term, however, relative to the exponent of the nonlocal nonlinear source.
文摘The nonlocal singularly perturbed nonlinear problem is considered. Underthe appropriate assumptions the author proved that there exists a solution andthe estimation of solution is obtained using the method of differential inequalities and a class of boundary layer functions.
文摘In this paper, we study a fractional differential equation cD0^a＋u（t）＋f（t,u（t））=0,t∈（0＋∞）satisfying the boundary conditions： ……where 1〈a≤2,cD0^a＋ is the standard Caputo fractional derivative of order a. The main tools used in the paper is a contraction principle in the Banach space and the fixed point theorem due to D. O＇Regan. Under a compactness criterion, the existence of solutions are established.
基金Supported by Foundation of Major Project of Science and Technology of Chinese Education Ministry(2005101SBJBC51)SRFDP of Higher Education(2005101TSJB157)
文摘考虑了非局部边值问题{-a(∫Ω|u|qdx)Δu+b(l(u))u=f(x,u), in Ω,u=0, on Ω,及其相应的非局部抛物问题的正解存在性.其中Ω是RN中的有界光滑区域,a和b是给定的函数.利用Galerkin方法,首先获得了具有低阶项的非局部椭圆问题正解的存在性,进一步证明了抛物问题正解的存在性.
基金Project supported by the National Natural Science Foundation of China
文摘The nonlocal theory which confiders interatomic long-range interaction in materials is one of the generalized continuum theories which involve the microstructure characteristic of material media. The basic equations of linear, homogeneous, isotropic, nonlocal elastic solids
