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.
Para recibir un certificado es necesario asistir al menos al 75% de las horas del curso y, además, inscribirse por correo electrónico a admin2-imus@us.es indicando lo siguiente:
Nombre de la actividad:
Nombre completo del participante:
DNI o pasaporte:
Correo electrónico:
