This article establishes the precise asymptotics Eu^m(t, x)(t → ∞ or m → ∞) for the stochastic heat equation ?u/?t(t, x) =1/2?u(t, x) + u(t, x)(t, x)?W/?t(t, x) with the time-derivative Gaussian noise W?/?t(t, x) ...This article establishes the precise asymptotics Eu^m(t, x)(t → ∞ or m → ∞) for the stochastic heat equation ?u/?t(t, x) =1/2?u(t, x) + u(t, x)(t, x)?W/?t(t, x) with the time-derivative Gaussian noise W?/?t(t, x) that is fractional in time and homogeneous in space.展开更多
The wave equations about displacement, velocity, stress and strain in functionally gradient material （FGM） with constituents varied continuously and smoothly were established. Four kinds of waves are of linear secon...The wave equations about displacement, velocity, stress and strain in functionally gradient material （FGM） with constituents varied continuously and smoothly were established. Four kinds of waves are of linear second-order partial differential equation of hyperbolic type and have the same characteristic curve at the plane of X,t. In general, the varying mode of stress is different from that of displacement and velocity at the front of wave. But in a special case that the product of density p and elastic modulus E of the material remains unchanged, the three wave equations have a similar expression and they have a similar varying mode in the front of wave.展开更多
In this paper, we present some necessary and sufficient conditions for the ex- istence of solutions, hermitian solutions and positive solutions to the system of operator equations AXB = C = BXA in the setting of bound...In this paper, we present some necessary and sufficient conditions for the ex- istence of solutions, hermitian solutions and positive solutions to the system of operator equations AXB = C = BXA in the setting of bounded linear operators on a Hilbert space. Moreover, we obtain the general forms of solutions, hermitian solutions and positive solutions to the system above.展开更多
基金Research partially supported by the “1000 Talents Plan” from Jilin University,Jilin Province and Chinese Governmentby the Simons Foundation(244767)
文摘This article establishes the precise asymptotics Eu^m(t, x)(t → ∞ or m → ∞) for the stochastic heat equation ?u/?t(t, x) =1/2?u(t, x) + u(t, x)(t, x)?W/?t(t, x) with the time-derivative Gaussian noise W?/?t(t, x) that is fractional in time and homogeneous in space.
基金the National Natural Science Foundation of China (No.50272046)
文摘The wave equations about displacement, velocity, stress and strain in functionally gradient material （FGM） with constituents varied continuously and smoothly were established. Four kinds of waves are of linear second-order partial differential equation of hyperbolic type and have the same characteristic curve at the plane of X,t. In general, the varying mode of stress is different from that of displacement and velocity at the front of wave. But in a special case that the product of density p and elastic modulus E of the material remains unchanged, the three wave equations have a similar expression and they have a similar varying mode in the front of wave.
基金supported by the National Natural Science Foundation of China(11371233)
文摘In this paper, we present some necessary and sufficient conditions for the ex- istence of solutions, hermitian solutions and positive solutions to the system of operator equations AXB = C = BXA in the setting of bounded linear operators on a Hilbert space. Moreover, we obtain the general forms of solutions, hermitian solutions and positive solutions to the system above.
