Department of Mathematics

Colloquium

  •  Nonlinear stability of sources
  •  10/05/2017
  •  4:10 PM - 5:00 PM
  •  C304 Wells Hall
  •  Björn Sandstede, Brown University

Defects are interfaces that mediate between two wave trains with possibly different wave numbers. Of particular interest in applications are sources for which the group velocities of the wave trains to either side of the defect point away from the interface. While sources are ubiquitous in experiments and can be found easily in numerical simulations of appropriate models, their stability analysis still presents many challenges. One difficulty is that sources are not travelling waves but are time-periodic in an appropriate moving coordinate frame. A second difficulty is that perturbations are transported towards infinity, which makes it difficult to apply various commonly used approaches. In this talk, I will discuss nonlinear stability results for sources in general reaction-diffusion system and outline a proof that utilizes pointwise estimates.

 

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Department of Mathematics
Michigan State University
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