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Seminários do IMPA

Análise / Equações Diferenciais Parciais

Linear instability of stationary solutions for the Korteweg–de Vries equation on a star graph
Jaime Angulo

Universidade de São Paulo
Quinta-feira, 16 de maio de 2019, 15:30
Sala 232

The aim of this conference is to establish a linear instability criterium of stationary solutions for the Korteweg–de Vries model on a star graph with a structure represented by a finite collections of semi-infinite edges. By considering a boundary condition of $\delta$-type at the graph-vertex, we show that the continuous bumps profiles are linearly unstable. The use of the analytic perturbation theory of operators and the extension theory of symmetric operators will be a piece fundamental in our stability analysis.

The arguments presented in this investigation have prospects for the study of the instability of stationary waves solutions of other nonlinear evolution equations on star graphs.