This article investigates the fractional derivative order identification, the coefficient identification, and the source identification in the fractional diffusion problems. If 1 〈 α〈 2, we prove the unique determi...
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This article investigates the fractional derivative order identification, the coefficient identification, and the source identification in the fractional diffusion problems. If 1 〈 α〈 2, we prove the unique determination of the fractional derivative order and the dif- fusion coefficient p（x） by fo u（0, s）ds, 0 〈 t 〈 T for one-dimensional fractional diffusion-wave equations. Besides, if 0 〈 α 〈 1, we show the unique determination of the source term f（x, y） by U（0, 0, t）, 0 〈 t 〈 T for two-dimensional fractional diffusion equations. Here, a denotes the fractional derivative order over t.
We study the double barrier tunneling properties of Dirac particles in spin-orbit coupled Bose–Einstein *** analytic expression of the transmission coefficient of Dirac particles penetrating into a double barrier is ...
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We study the double barrier tunneling properties of Dirac particles in spin-orbit coupled Bose–Einstein *** analytic expression of the transmission coefficient of Dirac particles penetrating into a double barrier is *** interesting resonance tunneling phenomenon is discovered in the Klein block region which has been ignored before.
The Cauchy problem for the massive Yang-Mills-Higgs equations is discussed. The existence and uniqueness of a kind of global radial solution for the problem are proved, where the Cauchy data depend on a pair of arbitr...
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The Cauchy problem for the massive Yang-Mills-Higgs equations is discussed. The existence and uniqueness of a kind of global radial solution for the problem are proved, where the Cauchy data depend on a pair of arbitrary functions.
Applying the integral a priori estimates method, the existence and uniqueness of the global solution for the system of the interaction of generalized long wave and short wave are proved. The approximate inertial manif...
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Applying the integral a priori estimates method, the existence and uniqueness of the global solution for the system of the interaction of generalized long wave and short wave are proved. The approximate inertial manifolds for this system are also constructed.
In this paper, relations between directional derivatives are considered for smooth functions both in 2D and 3D spaces. These relations are established in the form of linear combinations of directional derivatives with...
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In this paper, relations between directional derivatives are considered for smooth functions both in 2D and 3D spaces. These relations are established in the form of linear combinations of directional derivatives with their coefficients having simple form and structural regularity. By them, expressions based on directional derivatives for some typical differential operators are derived. This builds up a solid mathematical foundation for further study on numerical computation by the finite point method based on directional difference.
In this paper, we consider the long-time dynamics for the primitive equations of large-scale dry atmosphere. First, by energy methods, we obtain the existence and uniqueness of global strong solutions of the problem. ...
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In this paper, we consider the long-time dynamics for the primitive equations of large-scale dry atmosphere. First, by energy methods, we obtain the existence and uniqueness of global strong solutions of the problem. Second, by studying the long-time beha
We study the incompressible limit of classical solutions to compressible ideal magneto-hydrodynamics in a domain with a flat *** boundary condition is characteristic and the initial data is *** first establish the uni...
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We study the incompressible limit of classical solutions to compressible ideal magneto-hydrodynamics in a domain with a flat *** boundary condition is characteristic and the initial data is *** first establish the uniform existence of classical solutions with respect to the Mach ***,we prove that the solutions converge to the solution of the incompressible MHD *** particular,we obtain a stronger convergence result by using the dispersion of acoustic waves in the half space.
The following initial-boundary value problem for the systems with multidimensional inhomogeneous generalized Benjamin-Bona-Mahony ( GBBM ) equations is reviewed. The existence of global attractors of this problem was ...
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The following initial-boundary value problem for the systems with multidimensional inhomogeneous generalized Benjamin-Bona-Mahony ( GBBM ) equations is reviewed. The existence of global attractors of this problem was proved by means of a uniform priori estimate for time.
Multi-configuration Dirac-Fock and configuration interaction calculations in the extensive average level version with the inclusion of the transverse(Breit)interaction and low orders quantum electrodynamics have been ...
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Multi-configuration Dirac-Fock and configuration interaction calculations in the extensive average level version with the inclusion of the transverse(Breit)interaction and low orders quantum electrodynamics have been carried out for the wavelengths of five Ni-like laser *** ab initio results have been adjusted along the iso-electronic sequence and predict the *** predicted results have been compared and agree with available experimental values and may serve as road sign for experimentalists.
We provide a systematic study for the generalized Riemann problem(GRP)of the nonlinear hyperbolic balance law,which is critically concerned with the construction of the spatial-temporally coupled high-order Godunov-ty...
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We provide a systematic study for the generalized Riemann problem(GRP)of the nonlinear hyperbolic balance law,which is critically concerned with the construction of the spatial-temporally coupled high-order Godunov-type *** full analytical GRP solvers up to the third-order accuracy and also a collection of properties of the GRP solution are derived by resolving the elementary *** resolution of the rarefaction wave is a crucial point,which relies on the use of the generalized characteristic coordinate(GCC)to analyze the solution at the *** the analysis on the GCC,we derive for the general nonlinear system the evolutionary equations for the derivatives of generalized Riemann *** the nonsonic case,the full set of spatial and temporal derivatives of the GRP solution at the singularity are obtained,whereas for the sonic case the limiting directional derivatives inside the rarefaction wave are *** addition,the acoustic approximation of the analytical GRP solver is deduced by estimating the error it *** is shown that the computationally more efficient Toro-Titarev solver can be the approximation of the analytical solver under the suitable *** this work also provides a theoretical basis of the approximate GRP *** theoretical results are illustrated via the examples of the Burgers equation,the shallow water equations and a system for compressible flows under gravity *** results demonstrate the accuracy of the GRP solvers for both weak and strong discontinuity cases.
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