Special Session 64: Reaction-diffusion equations and applications

Uniform regularity estimates and inviscid limit for the compressible non-resistive magetohydrodynamics system

Xiufang Cui Lanzhou University Peoples Rep of China Co-Author(s):

Abstract: We are concerned with the uniform regularity estimates of solutions to the two dimensional compressible non-resistive magnetohydrodynamics equations with the no-slip boundary condition on velocity in the half plane. Under the assumption that the initial magnetic field is transverse to the boundary, the uniform conormal energy estimates are established for the solutions to compressible MHD equations with respect to the small viscosity coefficient. As a direct consequence. we proved the inviscid limit of solutions from viscous MHD equations to the ideal MHD system by some compact argument.

Accelerating propagation in diffusion phenomena

Wan-Tong Li Lanzhou University Peoples Rep of China Co-Author(s):

Abstract: In this talk, we focus on the accelerating propagation in diffusion phenomena. It is well-known that the solution of a monostable nonlocal dispersal scalar equation spreads at a finite speed when the kernel is light-tailed and propagates by accelerating when the kernel has a heavy-tail. However, in such systems, we find that one species can propagate by accelerating although its dispersal kernel is light-tailed, which is a new and interesting phenomenon. In particular, the accelerating phenomenon also has been found in nonlocal free boundary problems and in shifting environments.

Persistence and Spatial Propagation of an Impulsive Integro-differential System with Non-local Pulse

Jiabing Wang China University of Geosciences (Wuhan) Peoples Rep of China Co-Author(s):

Abstract: In order to investigate the spatial distribution and evolution dynamics of populations exhibiting synchronized reproduction and two stage long-distance dispersal modes, we propose an impulsive integro-differential system with non-local pulse. Firstly, we establish the extinction and persistence dynamics on the bounded domain with Dirichlet boundary of non-local type. Secondly,we derive the existence and characterization of the spreading speed in the whole space as well as the consistency with the minimum wave speed of the traveling waves in the case where the kernels are exponentially bounded. Thirdly, we study the accelerated propagation in the case where the dispersal kernel or pulse kernel is exponentially unbounded.

Spreading speeds of a nonlocal diffusive epidemic model with a new weight-type free boundary condition

Rong Wang Lanzhou University Peoples Rep of China Co-Author(s):    Xin Long

Abstract: This talk is concerned with the spreading behavior of a nonlocal epidemic model with new weight-type free boundary conditions. Such conditions were originally introduced for the Fisher--KPP equation in Du et al. (submitted, 2024), and they are used here to describe the expansion of the epidemic region under weighted population effects. This work continues a previous study by Long and Wang (submitted, 2026), in which the model was shown to be well posed and to exhibit a spreading--vanishing dichotomy in its long-time dynamics, together with a threshold condition for finite spreading speed. The main focus of this talk is the accelerated spreading case, where the spreading speed is infinite. For some typical classes of kernel and weight functions, I will present the precise rates of accelerated expansion of the epidemic region. This talk is based on joint work with Dr. Xin Long.

Long time behavior for Lotka-Volterra competiton-diffusion systems

Shi-Liang Wu xidian university Peoples Rep of China Co-Author(s):

Abstract: In this talk, we first introduce some known results on long time behavior of bounded solutions for reaction-diffusion equations. Then, we present our recent results on the long time behavior to Lotka-Volterra competition-diffusion systems.

The propagation dynamics for a class of time-period SIAR system with nonlocal dispersal and delay

Yun-Rui Yang Lanzhou Jiaotong University Peoples Rep of China Co-Author(s):    Meng-Xuan Jia

Abstract: In this talk, the propagation dynamics for a class of time-period SIAR system with nonlocal dispersal and delay are discussed. Firstly, the existence of asymptotic spreading speed is formed by the priori estimates, Arzela-Ascoli theorem, auxiliary systems and the uniform persistence idea for dynamical systems. Second, the existence of periodic traveling waves is established with the help of the non-compactness Kuratowski measure theory and the asymptotic fixed point theorem. Finally, the non-existence of periodic traveling waves is also obtained by a contradictory argument and analysis method.

An impulsive reaction-diffusion model with asymptotically bounded domain

Min Zhu Anhui Normal University Peoples Rep of China Co-Author(s):    Min Zhu and Xiao-Qiang Zhao

Abstract: In this talk, I will report our recent research on a continuous-discrete hybrid population model in a time-varying and asymptotically bounded domain. For the sake of analysis, this model is transformed into an impulsive reaction-diffusion system in a fixed domain. With the aid of the discrete-time semiflow generated by the solution maps of a limiting system and the theory of chain transitive sets, we establish the threshold-type results on the global dynamics of the model system in the cases of monotone and nonmonotone birth functions, respectively. Our explicit formula of the threshold value can help to understand how the final expansion factor of the habitat and the birth pulse rate affect the survival of population.