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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Homogenization of a front propagation model in dynamic environments
动态环境 前端传播模型 均质化 一阶哈密尔顿-雅可比方程
2023/4/18
In this talk I will review the developments of homogenization theory for a front propagation model. It is described by a first order Hamilton-Jacobi equation with a Hamiltonian that grows linearly wit...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：HT-Net: Hierarchical Transformer based Operator Learning Model for Multiscale PDEs
HT-Net 分层变压器 多尺度 偏微分方程 算子学习模型
2023/5/6
Complex nonlinear interplays of multiple scales give rise to many interesting physical phenomena and pose major difficulties for the computer simulation of multiscale PDE models in areas such as reser...
Wave-like solutions for nonlocal reaction-diffusion equations: a toy model
Traveling wave Wavetrains Nonlocal elliptic equations
2015/7/14
Traveling waves for the nonlocal Fisher Equation can exhibit much more complex behaviours than for the usual Fisher equation. A striking numerical observation is that a traveling wave with minimal spe...
Traveling Wave Solutions in a Reaction-Diffusion Model for Criminal Activity
Traveling Wave Solutions Reaction-Diffusion Model Criminal Activity
2015/7/14
We study a reaction-diffusion system of partial differential equations, which can be taken to be a basic model for criminal activity, first introduced in [3]. We show that the assumption of a populati...
Statistical Methods for Nonlinear Dynamic Models with Measurement Error Using the Ricker Model
measurement error ricker SIMEX
2014/12/8
In ecological population management, years of animal counts are fit to nonlinear, dynamic models (e.g. the Ricker model) because the values of the parameters are of interest. The yearly counts are sub...
Theory for the Rotational Deconvolution model of Turbulence with Fractional regularization
Theory the Rotational Deconvolution model Turbulence Fractional regularization Analysis of PDEs
2012/4/16
We introduce a new regularization of the rotational Navier-Stokes equations that we call the Rotational Approximate Deconvolution Model (RADM). We generalize the deconvolution type model, studied by B...
A Kind of Accelerated AOS Difference Schemes For Dual Currency Option Pricing Model
Dual currency option pricing model accelerated AOS algorithm 'explicit-implicit' scheme 'implicit-explicit' scheme second order accuracy
2011/10/15
Black-Scholes equation of Dual currency option pricing is a typical multi-asset option pricing model, and it is important to research it's numerical value. This paper uses the accelerated additive ope...
Analysis of the Leray-α model with Navier slip boundary condition
turbulence model existence weak solution
2011/9/22
Abstract: In this paper, we establish the existence and the regularity of a unique weak solution to turbulent flows in a bounded domain ${\Omega}\subset \mathbb R^3$ governed by the so-called Leray-{\...
Well-posedness for a multi-dimensional viscous gas-liquid two-phase flow model
Compressible gas-liquid two-phase flow model global well-posedness local well-posedness Besov spaces
2011/9/16
Abstract: The Cauchy problem of a multi-dimensional ($d\geqslant 2$) compressible viscous gas-liquid two-phase flow model is concerned in this paper. We investigate the global existence and uniqueness...
On a 3D isothermal model for nematic liquid crystals accounting for stretching terms
3D isothermal model nematic liquid crystals Analysis of PDEs
2011/9/15
Abstract: The present contribution investigates the well-posedness of a PDE system describing the evolution of a nematic liquid crystal flow under kinematic transports for molecules of different shape...
Periodic long-time behaviour for an approximate model of nematic polymers
Periodic long-time behaviour nematic polymers Analysis of PDEs
2011/9/14
Abstract: We study the long-time behaviour of a nonlinear Fokker-Planck equation, which models the evolution of rigid polymers in a given flow, after a closure approximation. The aim of this work is t...
Time relaxation of a phase-field model with entropy balance
phase-field model entropy balance Analysis of PDEs
2011/9/14
Abstract: We deal with a system of two coupled differential equations, describing the evolution of a first order phase transition. In particular, we have two non-linear parabolic equations: the first ...
Mathematical analysis of successive linear approximation for Mooney-Rivlin material model in finite elasticity
Linearized constitutive equations Mooney-Rivlin material Relative descriptional formulation Existence and uniqueness
2011/9/6
Abstract: For calculating large deformations in finite elasticity, we have proposed a method of successive linear approximation, by considering the relative descriptional formulation. In this article ...
On the Local Well-posedness of a 3D Model for Incompressible Navier-Stokes Equations with Partial Viscosity
3D Model Incompressible Navier-Stokes Equations Partial Viscosity Analysis of PDEs
2011/8/31
Abstract: In this short note, we study the local well-posedness of a 3D model for incompressible Navier-Stokes equations with partial viscosity. This model was originally proposed by Hou-Lei in \cite{...
Turing instabilities in a mathematical model for signaling networks
Turing instability non-local reaction-diffusion system signaling molecules
2011/8/30
Abstract: GTPase molecules are important regulators in cells that continuously run through an activation/deactivation and membrane-attachment/membrane-detachment cycle. Activated GTPase is able to loc...