Differential Equations Seminar

Classical nonlinear scalar field equations on the real line admit intriguing soliton solutions called kinks. The problem of their asymptotic stability leads to the study of the decay of small solutions to 1D Klein-Gordon equations with variable coefficient quadratic nonlinearities. In this talk I will discuss the occurrence of a novel modified scattering behavior of such solutions that involves a logarithmic slow-down of the decay rate along certain rays. It is caused by a striking resonant interaction between specific spatial frequencies of the variable coefficient and the temporal oscillations of the solutions.

This is joint work with H. Lindblad and A. Soffer.

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https://umich.zoom.us/j/98365676067

Meeting ID: 983 6567 6067
Passcode: 2020 Speaker(s): Jonas Luhrmann (Texas A&M)