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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On strongly quasiconvex functions: existence results and proximal point algorithms
强准孔函数 存在结果 近端点算法
2023/5/4
The class of strongly quasiconvex functions was introduced in the famous paper of B.T. Polyak in 1966. It is the natural extension of the class of strongly convex functions, its applications emcompass...
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...
Existence of solutions for a higher order non-local equation appearing in crack dynamics
Hydraulic fractures Higher order equation Non-local equation Thin film equation Non-negative solutions periodic Hilbert transform
2015/10/15
In this paper, we prove the existence of non-negative solutions for a non-local higher order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to th...
Existence and regularity of extremal solutions for a mean-curvature equation
Mean curvature minimal solution semi-stable solution extremal solution regularity
2015/10/15
We study a class of mean curvature equations −Mu = H +λup where M denotes the mean curvature operator and for p ≥ 1. We show that there exists an extremal parameter λ∗ such that this equat...
Electrified thin films:Global existence of non-negative solutions
Higher order equation Non-local equation Thin film equation Non-negative solutions
2015/10/15
We consider an equation modeling the evolution of a viscous liquid thin film wetting a horizontal solid substrate destabilized by an electric field normal to the substrate. The effects of the electric...
EXISTENCE AND ASYMPTOTICS OF FRONTS IN NON LOCAL COMBUSTION MODELS
EXISTENCE ASYMPTOTICS NON LOCAL COMBUSTION MODELS
2015/10/15
We prove the existence and give the asymptotic behavior of non local fronts in homogeneous media.
EXISTENCE OF WEAK SOLUTIONS TO KINETIC FLOCKING MODELS
flocking kinetic equations existence velocity averaging CuckerSmale self-organized dynamics
2015/10/15
We establish the global existence of weak solutions to a class of kinetic flocking equations. The models under conideration include the kinetic Cucker-Smale equation [6, 7] with possibly non-symmetric...
The Existence of Pair Potential Corresponding to Specified Density and Pair Correlation
Gibbs Field Gibbs Measure Cluster Functions Pair Potential Corrlation Functions Ursell Functions
2015/9/28
Given a potential of pair interaction and a value of activity, one can consider the Gibbs distribution in a finite domain Λ ⊂ Z d . It is well known that for small values of activity there...
Traveling fronts in porous media: existence and a singular limit
Traveling fronts porous media existence singular limit
2015/7/14
We consider a model for the propagation of a subsonic detonation wave through a porous medium introduced by Sivashinsky [8]. We show that it admits travelling wave solutions that converge in the limit...
Existence of pulsating waves in a model of flames in sprays
pulsating waves model of flames in sprays
2015/7/14
A one-dimensional system describing the propagation of low Mach number flames in sprays is studied. We show that pulsating waves may exist when the droplet distribution in the unburnt region is spatia...
Existence and Non-existence of Fisher-KPP Transition Fronts
Existence Non-existence Fisher-KPP
2015/7/14
We consider Fisher-KPP-type reaction-diffusion equations with spatially inhomogeneous reaction rates. We show that a sufficiently strong localized inhomogeneity may prevent existence of transition-fro...
The Existence of MLE in Location and Dispersion Effects Models with Censored Data
MLE in Location and Dispersion Effects Models Censored Data
2015/3/20
The Existence of MLE in Location and Dispersion Effects Models with Censored Data.
Existence, Stability, and Dynamics of Solitary Waves in Nonlinear Schroedinger Models with Periodic Potentials
Non-square lattices, Nonlinear waves Photonic lattices
2014/12/8
The focus of this dissertation is the existence, stability, and resulting dynamical evolution of localized stationary solutions to Nonlinear Schr¨odinger (NLS) equations with periodic confining potent...
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...
On the existence and number of $(k+1)$-kings in $k$-quasi-transitive digraphs
digraph k-king quasi-transitive digraph k-quasi-transitive digraph
2012/6/30
Let $D=(V(D), A(D))$ be a digraph and $k \ge 2$ an integer. We say that $D$ is $k$-quasi-transitive if for every directed path $(v_0, v_1,..., v_k)$ in $D$, then $(v_0, v_k) \in A(D)$ or $(v_k, v_0) \...