Abstract : In this minisymposium we will focus on recent progress about the theory and applications of
reaction-diffusion systems. A special focus will on the mathematical modelling and analysis for evolution systems with applications in biological, ecological, health and medical sciences such as modelling infectious diseases and tumor growth in life sciences. The minisymposium will invite experts in the field to report their recent results on these subjects.
Organizer(s) : Hong-Ming Yin, Takashi Suzuki, Yihong Du
[01711] Propagation dynamics of the Fisher-KPP nonlocal diffusion equation with free boundary
Format : Talk at Waseda University
Author(s) :
Yihong Du (University of New England)
Abstract : Propagation has been modelled by reaction-diffusion equations since the pioneering works of Fisher and Kolmogorov-Peterovski-Piskunov (KPP). Much new developments have been achieved in the past several decades on the modelling of propagation, with traveling wave and related solutions playing a central role. In this talk, I will report some recent results obtained with several collaborators on the Fisher-KPP equation with free boundary and "nonlocal diffusion", where the diffusion operator is given by a convolution integral instead of the traditional Laplacian operator. A key feature of this nonlocal equation is that the propagation may or may not be determined by traveling wave solutions. There is a threshold condition on the kernel function in the diffusion operator which determines whether the propagation rate is linear or superlinear in time, also known as accelerated spreading in the latter case, where the rate of spreading is not determined by traveling waves. For some typical kernel functions, sharp spreading rates will be presented.
[03297] propagation phenomena of fractional diffusion equations
Format : Talk at Waseda University
Author(s) :
Xing Liang (University of Science and Technology of China)
Abstract : In this talk, I will introduce our works on the propagation phenomena of fractional diffusion equations. The first part is about KPP-type equations in almost periodic media. We will show the existence of exponential speeds of propagation and a counterintuitive conclusion that faster diffusion yields slower propagation. The second part is about bistable and multi-stable equation in periodic media. We will show the existence of the traveling terrace and when the traveling terrace becomes a traveling wave.
[02984] Sharp traveling waves for degenerate equations with time-delay: Fisher-KPP equations and Burgers equations
Format : Talk at Waseda University
Author(s) :
Ming Mei (McGill University & Champlain College)
Abstract : In this talk, we are concerned with the degenerate diffusion equations with time-delay. The typical examples include Fisher-KPP equations and Burgers equations. The main issue is to investigate the structure of traveling waves, which are the sharp traveling waves with oscillations. The sharpness is caused by the degeneracy of diffusion, and oscillation is caused by the large time-delay.
[03485] Accelerating propagation in a nonlocal model with periodic time delay
Format : Talk at Waseda University
Author(s) :
Jian Fang (Harbin Institute of Technology)
Abstract : In this talk, we investigate the accelerating propagation dynamics of a nonlocal population model with periodic time delay, which may arise from the study of stage-structured invasive species subject to seasonal successions. After establishing the fundamental solution of related linear equation, we obtain a sharp estimate for the solution level set.
[01484] Recent Progress on Reaction-Diffusion Systems and Applications in Life Sciences
Format : Talk at Waseda University
Author(s) :
Hong-Ming Yin (Washington State University)
Abstract : Reaction-diffusion equations and systems are the backbone of many mathematical models in biological, ecological, health and medical sciences. In this talk I will first give a short survey on some recent progress about the global solvability for general reaction-diffusion systems. Then I will focus on a class of nonlinear reaction-diffusion systems with balanced mass. Some new results will be reported in the talk. Finally, I will show how the general result is used to establish the global solvability for two models arising from life sciences.
[04053] Effect of density-dependent dispersal on the predator-prey system
Format : Talk at Waseda University
Author(s) :
Zhi-An Wang (The Hong Kong Polytechnic University )
Abstract : This talk is concerned with existence, non-existence and uniqueness of positive (coexistence) steady states to a predator-prey system with density-dependent dispersal. By our analysis results, we pinpoint the positive role of density-dependent dispersal on the predator-prey dynamics for the first time and show that the density-dependent dispersal is a beneficial strategy promoting the coexistence of species in the predator-prey system by increasing the chance of predator's survival.
[04100] Nonlinear Stefan problem with a certain class of multi-stable nonlinearity
Format : Talk at Waseda University
Author(s) :
Hiroshi Matsuzawa (Kanagawa University)
Yuki Kaneko (Kanto Gakuin University)
Yoshio Yamada (Waseda University)
Abstract : I will discuss the long-time dynamical behavior of solutions to a nonlinear Stefan problem for a reaction-diffusion equation with a positive bistable type nonlinearity. I will show that the asymptotic behavior of the solutions is classified into four cases: vanishing, small spreading, big spreading, and transition. In particular, I will show that for transition occurs, the solution converges to an equilibrium solution that is radially symmetric, radially decreasing, and centered at some point as $t\to\infty$.
[01531] Some results on a haptotaxis model of cancer invasion
Format : Online Talk on Zoom
Author(s) :
Feng Dai ( Huazhong University of Science and Technology)
Abstract : In this talk, we will report some results on a haptotaxis model of cancer invasion. Under appropriate
regularity assumptions on initial data, the global solvability of the corresponding homogeneous Neumann
initial-boundary value problem is established. In addition, an optimal control problem for this cancer
invasion model with chemotherapy is investigated to balance the therapeutic benefits with its side effects.
Juan B Gutierrez (University of Texas at San Antonio)
Abstract : In this talk, I present a framework that describes the necessary and sufficient conditions for propagation of one or more undesirable species, named here the nonconformist species, in a given environment when there is an intervention trying to counter their propagation. We assume that the dispersal of the nonconformist could be characterized by a reaction-diffusion process, whereas there is no spatial dependence for the action of the countermeasures. I present a generalized method that can analyze an arbitrary number of nonconformist species and countermeasures.
