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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Uniqueness of BV Solution for Compressible Euler Equations
可压缩 欧拉方程 BV解 唯一性
2023/4/17
Compressible Euler equations are a typical system of hyperbolic conservation laws, whose solution forms shock waves in general. It is well known that global BV solutions of system of hyperbolic conser...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stokes phenomenon and isomonodromy deformation equations: Explicit solution to the Riemann-Hilbert problem and integrability of the isomonodromy equation
斯托克斯现象 等单向变形方程 黎曼-希尔伯特问题 显式解 单场方程 可积性
2023/5/6
Stokes phenomenon states that the asymptotic behavior of functions can differ in different regions of the complex plane, and that these differences can be described in a quantitative way. These quanti...
Accelerated solution of the frequency-domain Maxwell’s equations by engineering the eigenvalue distribution of the operator
Numerical approximation analysis Mathematical methods physics Mathematics
2015/8/7
We introduce a simple method to accelerate the convergence of iterative solvers of the frequency-domain Maxwell’s equations for deep-subwavelength structures. Using the continuity equation, the method...
Solution of the Cauchy problem for the Navier - Stokes and Euler equations
Solution Cauchy problem the Navier - Stokes Euler equations
2010/12/3
Some known results regarding the Euler and Navier-Stokes equations were obtained by different authors.Existence and smoothness of the Navier-Stokes solutions in two dimensions have been known for a lo...
Bilinear Equations and Bäcklund Transformation for Generalized Ultradiscrete Soliton Solution
Bilinear Equations Bä cklund Transformation Generalized Ultradiscrete Soliton Solution
2010/4/2
Ultradiscrete soliton equations and B\"acklund transformation for a generalized soliton solution are presented. The equations include the ultradiscrete KdV equation or the ultradiscrete Toda equation ...
Fundamental Solution Global in Time for a Class of Schrödinger Equations with Time-Dependent Potentials
Schrö dinger equation fundamental solution Fourier integral operators long-range potentials scattering theory
2008/11/25
Fundamental solution for a Schrödinger equation with a time-dependent potential of
long-range type is constructed. The solution is given as a Fourier integral operator with
a symbol uniformly b...
Smooth Dependence by LAG of the Solution of a Delay Integro-Differential Equation from Biomathematics
neutral delay integro-differential equation Perov’s fixed point theorem Picard operators successive approximations sequence smooth dependence by lag
2008/11/25
Using the Perov’s fixed point theorem and the theorem of fiber generalized contractions,
we obtain the smooth dependence by lag of the positive periodic solution
of a neutral delay integro-different...
In this paper we prove the solution of explicit difference scheme for a
semilinear parabolic equation converges to the solution of difference
scheme for the relevant nonlinear stationary problem as ...
LONG TIME ASYMPTOTIC BEHAVIOR OF SOLUTION OF DIFFERENCE SCHEMEFOR A SEMILINEAR PARABOLIC EQUATION
Asymptotic behavio implicit difference scheme semilinear parabolic equation
2007/12/12
In this paper we prove that the solution of implicit difference scheme
for a semilinear parabolic equation converges to the solution of
difference scheme for the corresponding nonlinear stationary...