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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...
Existence and uniqueness of global strong solutions for one-dimensional compressible Navier-Stokes equations
global strong solutions one-dimensional compressible Navier-Stokes equations
2015/10/15
We consider Navier-Stokes equations for compressible viscous fluids in one dimension. It is a well known fact that if the initial datum are smooth and the initial density is bounded by below by a posi...
ON UNIQUENESS OF SOLUTION OF A n-TH ORDER DIFFERENTIAL EQUATION IN CONFORMAL GEOMETRY
ON UNIQUENESS OF SOLUTION A n-TH ORDER DIFFERENTIAL EQUATION CONFORMAL GEOMETRY
2014/4/3
In this paper, we prove an uniqueness theorem for a n-th order elliptic equation on the standard n-sphere Sn. The problem arises naturally from the point of view of conformal geometry. The method we u...
Existence, uniqueness, universality and functoriality of the perfect locality over a Frobenius P-category
Existence functoriality of the perfect locality Frobenius P-category Group Theory
2012/7/9
Let p be a prime, P a finite p-group and F a Frobenius P-category. The question on the existence of a suitable category L^sc extending the full subcategory of F over the set of F-selfcentralizing subg...
The lasso is a popular tool for sparse linear regression, especially for problems in which the number of variables p exceeds the number of observations n. But when p>n, the lasso criterion is not stri...
On the Comparison and Uniqueness for Solutions of BSDEs with Continuous Coefficients
Backward stochastic differential equation comparison theorem uniqueness
2011/11/5
As we known that there may be more than one solution for backward stochastic differential equation with continuous coefficients and the comparison theorem for any solutions of two BSDEs does not hold ...
Generalized Ricci flow I: Local existence and uniqueness
Generalized Ricci flow uniformly parabolic system short-time existence Thurston’s eight geometries
2018/4/19
In this paper we investigate a kind of generalized Ricci flow which possesses a gradient form. We study the monotonicity of the given function under the generalized Ricci flow and prove that the relat...
Uniqueness of compact tangent flows in Mean Curvature Flow
compact tangent flows Mean Curvature Flow Differential Geometry
2011/9/19
Abstract: We show, for mean curvature flows in Euclidean space, that if one of the tangent flows at a given spacetime point consists of a closed, multiplicity-one, smoothly embedded self-similar shrin...
Local Uniqueness of the Circular Integral Invariant
Integral invariants curves curve descriptors
2011/9/16
Abstract: This article is concerned with the representation of curves by means of integral invariants. In contrast to the classical differential invariants they have the advantage of being less sensit...
Transport equations with fractal noise - existence, uniqueness and regularity of the solution
Stochastic partial differential equations Transport equation Nonsmooth coefficients Fractional Brownian noise
2011/9/15
Abstract: The main result of the present paper is a statement on existence, uniqueness and regularity for mild solutions to a parabolic transport diffusion type equation that involves a non-smooth coe...
Generalized Ricci flow I: Local existence and uniqueness
Generalized Ricci flow uniformly parabolic system short-time existence Thurston’s eight geometries
2011/9/13
Abstract: In this paper we investigate a kind of generalized Ricci flow which possesses a gradient form. We study the monotonicity of the given function under the generalized Ricci flow and prove that...
Some uniqueness results for stationary solutions to the Maxwell-Born-Infeld field equations and their physical consequences
stationary solutions the Maxwell-Born-Infeld field equations Analysis of PDEs
2011/9/5
Abstract: Uniqueness results are established for time-independent finite-energy electromagnetic fields which solve the nonlinear Maxwell--Born--Infeld equations in boundary-free space under the condit...
Existence and uniqueness of very singular solutions for a fast diffusion equation with gradient absorption
Very singular solution singular diffusion gradient absorption self-similar solutions p-Laplacian uniqueness
2011/8/26
Abstract: Existence and uniqueness of radially symmetric self-similar very singular solutions are proved for the singular diffusion equation with gradient absorption {equation*} \partial_t u -\Delta_{...
Resonant uniqueness of radial semiclassical Schrodinger operators
inverse scattering theory trace invariants semiclassical Schrodinger operators
2011/8/25
Abstract: We prove that radial, monotonic, superexponentially decaying potentials in R^n, n greater than or equal to 1 odd, are determined by the resonances of the associated semiclassical Schrodinger...
Some results on zeros distributions and uniqueness of derivatives of difference polynomials
Zeros difference polynomials derivatives value sharing uniqueness
2011/8/25
Abstract: We consider the zeros distributions on the derivatives of difference polynomials of meromorphic functions, and present some results which can be seen as the discrete analogues of Hayman conj...