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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Mixing flow and advection-diffusion-reaction equations
混合流 平流 扩散反应方程
2023/5/18
In the study of incompressible fluid, one fundamental phenomenon that arises in a wide variety of application is dissipation enhancement by so-called mixing flow. In this talk, I will give a brief int...
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...
Diffusion Based Modeling of Human Brain Response to External Stimuli
Diffusion Modeling of Human Brain External Stimuli Analysis of PDEs
2012/4/18
Human brain response is the overall ability of the brain in analyzing internal and external stimuli in the form of transferred energy to the mind/brain phase-space and thus, making the proper decision...
The influence of fractional diffusion in Fisher-KPP equations
influence fractional diffusion Fisher-KPP equations
2012/2/29
We study the Fisher-KPP equation where the Laplacian is replaced by the generator of a Feller semigroup with power decaying kernel, an important example being the fractional Laplacian. In contrast wit...
Total Variation Flow and Sign Fast Diffusion in one dimension
Fast Diffusion Total Variation Flow asymptotic extinction profile convergence rates extinction time
2011/9/1
Abstract: We consider the dynamics of the Total Variation Flow (TVF) $u_t=\div(Du/|Du|)$ and of the Sign Fast Diffusion Equation (SFDE) $u_t=\Delta\sign(u)$ in one spatial dimension. We find the expli...
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_{...
Global solutions to a non-local diffusion equation with quadratic non-linearity
Global solutions a non-local diffusion equation quadratic non-linearity
2011/1/21
In this paper we prove the global in time well-posedness of the following non-local diffusion equation with ∈ [0, 2/3):@tu = (−△)−1u △u + u2, u(t = 0) = u0.
Elliptic operators with unbounded diffusion coefficients in Lp spaces
elliptic operators unbounded coefficients generation results analytic semigroups
2010/12/1
In this paper we prove that, under suitable assumptions on > 0, the operator L = (1+|x| ) admits realizations generating contraction or analytic semigroups in Lp(RN). For some values of , we also ...
On zero-sum Stochastic Differential Games with Jump-Diffusion driven state: A viscosity solution framework
Stochastic differential games L´ evy processes dynamic programming
2010/12/13
A zero-sum differential game with controlled jump-diffusion driven state is considered, and studied using a combination of dynamic programming and viscosity solution techniques. We prove, under certai...
This paper presents a class of high resolution local time step
schemes for nonlinear hyperbolic conservation laws and the closely
related convection--diffusion equations, by projecting the
solution...
THE GLOBAL DUFORT-FRANKEL DIFFERENCE APPROXIMATION FOR NONLINEAR REACTION-DIFFUSION EQUATIONS
globel Dufort-Frankel method reaction-diffusion eqution global attractor error estimate numerical experiments
2007/12/12
In this paper, the initial value problem of nonlinear reaction-diffusion
equation is considered. The Dufort-Frankel finite difference
approximation for the long time scheme is given for the $d$-dime...
Anticipative Stochastic Differential Equations with Non-smooth Diffusion Coefficient
Non-smooth and anticipative stochastic differential equations Skorohod integral Malliavin derivative
2007/12/11
In this paper we prove the existence and uniqueness of the solutions to the one-dimensional linear stochastic differential equation with Skorohod integral $$\ \ X_t(\omega )=\eta (\omega )+ \int^t_0 a...
Convergence to Diffusion Waves for Nonlinear Evolution Equations with Ellipticity and Damping, and with Different End States
evolution equations diffusion waves decay rate energy method a priori estimates
2007/12/11
In this paper, we consider the global existence and the asymptotic behavior of solutions to the Cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects:...
Internal Stabilization of A Mutualistic Reaction Diffusion System
stabilization mutualistic systems steady-state solution Riccati equation feedback controller
2007/12/11
We study the internal stabilization of steady-state solutions to a 2-species mutualistic reaction diffusion system via finite-dimensional feedback controllers. Our main idea is to use different intern...