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NCTS Webinar on Nonlinear Evolutionary Dynamics
 
14:30 - 16:00, April 16, 2025 (Wednesday)
Cisco Webex, Online seminar
(線上演講 Cisco Webex)
Computer-assisted Proofs for Periodic Traveling Waves in Higher Dimensional Partial Differential Equations
Lindsey van der Aalst (Vrije Universiteit Amsterdam)

Abstract
The one-dimensional suspension bridge equation has been well studied: traveling waves of various types have been proven to exist. Far less is known about the two-dimensional case. We use computer-assisted proof methods to find and prove periodic traveling waves in two spatial dimensions, ensuring rigorous control over computational errors.
Additionally, we extend computer-assisted proof techniques from existing literature on two-dimensional periodic solutions in the forced Navier-Stokes equations to three dimensions to prove traveling wave solutions. Challenges posed by the higher-dimensional nature of the problem are alleviated by employing symmetry arguments.
 
WebEx Link: TBA 
 
Organizers: Chueh-Hsin Chang (CCU), Jia-Yuan Dai (NTHU), Bo-Chih Huang (CCU), Chih-Chiang Huang (CCU), Alejandro López-Nieto (NTU), Chang-Hong Wu (NYCU)
 


 

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