Nonlinear Waves Seminar - Yifeng Mao

Yifeng Mao, Department of Applied Mathematics, University of Colorado Boulder

Long-time asymptotics and the radiation condition for time-periodic linear boundary value problems

Initial-boundary value problems (IBVPs) with constant initial and time-dependent boundary data, also known as the wavemaker problem, are fundamental and of significant importance in mathematics and physics. For the linear time-periodic wavemaker problem, the radiation condition selects the unique traveling wave or spatially decaying wave in the neighborhood of the boundary. However, this simple and physically plausible argument has yet to be mathematically justified in a general context. In recent work, the IBVP for some linear and integrable nonlinear evolution equations has been solved using the unified transform method. A related approach, called the Q-equation method, has been introduced to derive the Dirichlet-to-Neumann (D-N) map for asymptotically time-periodic boundary conditions. This talk will extend and prove the existence of the unique D-N map for a general third-order wave model and prove the radiation condition as a consequence. In addition, two representative linear evolution equations with sinusoidal boundary conditions are studied and uniform asymptotic approximations are obtained for large t, one of which is shown to give a quantitative description of wavemaker experiments.

Dial-In Information 

Tuesday, October 3, 2023 at 4:00pm to 5:00pm

Engineering Center, ECOT 317
1111 Engineering Drive, Boulder, CO 80309

Event Type



Science & Technology, Research & Innovation


Students, Graduate Students

College, School & Unit

Engineering & Applied Science


nonlinear waves seminar

Applied Mathematics
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