instituto de matemáticas universidad de sevilla
Antonio de Castro Brzezicki
Bifurcation theory and its applications in PDEs and mathematical biology
Actividad del Programa de Doctorado
Fecha: Del 15.10.2018 al 19.10.2018 De 10.00 a 12.30
Lugar: Instituto de Matemáticas de la Universidad de Sevilla (IMUS)

 Lunes 15 octubre de 10:00 a 11:30 horas en Seminario II IMUS.

 Martes 16 de octubre de 10:00 a 11:30 en Seminario II IMUS y de 16:00 a 17:30 horas en Seminario I IMUS.

 Miércoles 17 de octubre de 16:00 a 17:30 horas en Seminario I IMUS.

 Jueves 18 de octubre de 10:00 a 11:30 horas en Seminario I IMUS. 

 Viernes 19 de octubre de 11:00 a 12:30 horas en Semimnario I IMUS.

Abstract: In mathematical models from physical or biological applications, non-homogeneous states often arise as a result of symmetry breaking from homogeneous states, which is called bifurcation phenomenon. Some classical and new abstract bifurcation theorems, including local, global, and Hopf bifurcations, will be reviewed or introduced; secondly we show some applications of these results in nonlinear partial differential equations arising from biological systems, and we focus on the effect of diffusion, advection, taxis and nonlocal terms on the dynamics. When possible, we also show the global bifurcation structure and exact multiplicity of steady state solutions. If time allows, we will also introduce the results on delay differential equations with diffusion effect. The course is suitable for graduate students in nonlinear partial differential equations and mathematical biology who are familiar with partial differential equations, dynamical systems and functional analysis. There will be 6 lectures and each lecture is about 90 minutes.

1. Abstract bifurcation theory for stationary problems.
2. Turing type bifurcations.
3. Global bifurcation and exact multiplicity.
4. Hopf bifurcations.
5. Beyond diffusion: advection, taxis, and nonlocal effect.
6. Delay differential equations.

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