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The Sino-French International Associated Laboratory for Applied Mathematics (LIASFMA) is pleased to announce the School and Workshop on Harmonic Analysis and Wave Equations at Fudan University, Shangh...
International Workshop on Nonlinear Analysis and Reaction-Diffusion Equations
International Workshop Nonlinear Analysis and Reaction-Diffusion Equations
2017/3/28
“International Workshop on Nonlinear Analysis and Reaction-Diffusion Equations”, is to be held at Jiangsu University, Zhenjiang, China, June 3-5, 2017 (with June 2nd as registration day). The aim of t...
Generalized Iteration Method for First-Kind Integral Equations
Generalized Iteration Method First-Kind Integral Equations
2015/10/16
An iteration method is described to solve one-dimensional, first-kind integral equations with finite integration limits and difference kernel, K(x − x), that decays exponentially. The method re...
Global weak solutions for a Vlasov-Fokker-Planck/Navier-Stokes system of equations
Global weak solutions Vlasov-Fokker-Planck Navier-Stokes system of equations
2015/10/15
We establish the existence of a weak solutions for a coupled system of kinetic and fluid equations. More precisely, we consider a Vlasov-FokkerPlanck equation coupled to compressible Navier-Stokes equ...
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...
A bound from below for the temperature in compressible Navier-Stokes equations
below for the temperature compressible Navier-Stokes equations
2015/10/15
We consider the full system of compressible Navier-Stokes equations for heat conducting fluid. We show that the temperature is uniformly positive for t ≥ t0 (for any t0 > 0) for any solutions with fin...
Second kind integral equations for the first kind Dirichlet problem of the biharmonic equation in three dimensions
Second kind integral equation Dirichlet problem Biharmonic equation
2015/7/14
A Fredholm second kind integral equation (SKIE) formulation is constructed for the Dirichlet problem of the biharmonic equation in three dimensions. A fast numerical algorithm is developed based on th...
A sweeping preconditioner for Yee’s finite difference approximation of time-harmonic Maxwell’s equations
Electromagnetic scattering Yee grid finite difference methods perfectly matched layers LDLT factorizations multifrontal method wave propagation in inhomogeneous and anisotropic media matrix preconditioners
2015/7/14
This paper is concerned with the fast iterative solution of linear systems arising from finite difference discretizations in electromagnetics. The sweeping preconditioner with moving perfectly matched...
A sweeping preconditioner for time-harmonic Maxwell’s equations with finite elements
Maxwell’s equations Frequency domain Finite element methods Preconditioners Fast solvers Perfectly matched layers Block LDLt factorization High-frequency waves
2015/7/14
This paper is concerned with preconditioning the stiffness matrix resulting from finite element discretizations of Maxwell’s equations in the high frequency regime. The moving PML sweeping preconditio...
A PARALLEL SWEEPING PRECONDITIONER FOR HETEROGENEOUS 3D HELMHOLTZ EQUATIONS
Helmholtz time-harmonic sweeping preconditioner parallel
2015/7/14
A parallelization of a sweeping preconditioner for 3D Helmholtz equations without internal resonance is introduced and benchmarked for several challenging velocity models. The setup and application co...
Time splitting for wave equations in random media
Time splitting wave equations random media
2015/7/14
Numerical simulation of high frequency waves in highly heterogeneous media is a challenging problem. Resolving the fine structure of the wave field typically requires extremely small time steps and sp...
Quenching and propagation in KPP reaction-diffusion equations with a heat loss
Quenching and propagation KPP reaction-diffusion equations heat loss
2015/7/14
We consider a reaction-diffusion system of the KPP type in a shear flow and with a non-zeroheat loss parameter. We establish criteria for the flame blow-off and propagation, and identify the propagati...
A short proof of the logarithmic Bramson correction in Fisher-KPP equations
logarithmic Bramson correction Fisher-KPP equations
2015/7/14
In this paper, we explain in simple PDE terms a famous result of Bramson about the logarithmic delay of the position of the solutions u(t, x) of Fisher-KPP reaction-diffusion equations in R, with resp...
Power-like delay in time inhomogeneous Fisher-KPP equations
Power-like delay time inhomogeneous Fisher-KPP equations
2015/7/14
We consider solutions of the KPP equation with a time-dependent diffusivity of the formσ(t/T). For an initial condition that is compactly supported, we show that when σ(s) is increasing in time the fr...
Solving Quadratic Equations via PhaseLift when There Are About As Many Equations As Unknowns
Solving Quadratic Equations PhaseLift Many Equations Unknowns
2015/6/17
This note shows that we can recover any complex vector x0 ∈ Cn exactly from on the order of n quadratic equations of the form |hai, x0i|2 = bi, i = 1, . . . , m, by using a semidefinite program known ...