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NCTS Webinar on Nonlinear Evolutionary Dynamics
10:00 - 12:00, May 31, 2023 (Wednesday)
Cisco Webex, Online seminar
(線上演講 Cisco Webex)
Spreading Phenomena in Nonlocal Diffusion Equations with Free Boundaries in High Dimensions
Wenjie Ni (University of New England)


In this talk, I will discuss the intriguing behavior of nonlocal diffusion equations with free boundaries in high dimensions. These equations exhibit a "spreading-vanishing" dichotomy in their long-term solutions, reminiscent of local problems. However, a remarkable distinction arises in the determination of the spreading front's speed, which can reach infinity, unlike in local problems. My collaborator, Professor Du, and I have obtained improved estimates for the spreading speed, both finite and infinite, particularly focusing on kernel functions behaving like |x|r near infinity. Our findings represent the first results of their kind for this class of free boundary problems, and we have also investigated the spreading speed in high-dimensional settings.
Meeting number (access code): 2518 320 5961
Meeting password: VCv8Q5VA5kx


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