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Seminario de prelectura de tesis

## Seminario de prelectura de tesis

Doctorando: Alejandro Gárriz Molina
Director: Fernando Quirós Gracián



Título: Large time behaviour in local and non-local diffusion
Fecha: 4 de noviembre de 2020, 11:30
Lugar: ONLINE, mediante una reunión virtual en el equipo de Microsoft Teams titulado "Prelectura tesis Alejandro Gárriz Molina (4 de noviembre)"

Si no sois miembros del equipo y queréis asistir, por favor escribid por email a This email address is being protected from spambots. You need JavaScript enabled to view it.

Resumen: During this session we will discuss several different diffusion models, both local and non-local, paying special attention to the behaviour of their solutions for big times.

In the local case we will study the existence of wavefronts for the equations of the family
$$u_t=Delta_p a(u) + abla b(u) + c(u), p>1$$
and later on these wavefronts will be used to determine the asymptotic behaviour of the solutions of the equation
$$u_t = Delta_p u^m + h(u), m(p-1)>1, p>2,$$
in dimension $Ngeq 1$, where $h(u)$ is a reaction term  (generally, either monostable, bistable or combustion type) whenever the solutions converge uniformly to 1, a question that will also be addressed in the session.

In the non-local case we will present two new models where two different operators are acting on different domains but are intertwined by a third non-local one, receiving the name of coupling models. The first model will present the coupling of a heat operator and an operator given by the convolution with a probability kernel, while the second will study the coupling of two fractional laplacians of different order coupled by a third one. In both cases questions about the existence of solutions, the decay rates of the $L^p$ norms of the solutions or the large time behaviour of them will be addressed, together with other questions about these novel models.
Location Fecha: 4 de noviembre de 2020, 11:30