Online Analysis and PDE seminar

  • Biweekly seminar series, bringing together those within the field of Analysis and PDEs to present their work.

  • Runs 15:00-16:00 on Wednesdays, hosted by the Faculty of Science of University of Cantabria using Microsoft TEAMS.

  • Organized by:
    Universidad Autónoma de Madrid (UAM)
    Universidad de Cantabria (UC)
    Universidad Carlos III (UC3M)
    Universidad Complutense de Madrid (UCM)
    Instituto de Ciencias Matemáticas (ICMAT)
    Instituto de Matemáticas de la Universidad de Sevilla (IMUS)

Instructions to attend the seminar:
1) join the mailing list by writing an email to onlineapdeseminar(at)gmail(dot)com. You only need to do this once.
2) download Microsoft TEAMS and register yourself. You will not need a license.
3) you will receive an email with the link to join the talk a couple of hours before the starting time.
We also ask for your patience with any technical difficulties.


UPCOMING TALK

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Wednesday 7th April at 15:00 (CET)

José M. Mazón
(Universidad de Valencia)

Title: Multiscale decomposition of functions in Metric Random Walk Spaces
Abstract:


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TALKS TO COME

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  • Wednesday 21th April at 15:00 (CET)

TBA
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  • Wednesday 5th May at 15:00 (CET)

TBA
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  • Wednesday 19th May at 15:00 (CET)

Philippe Souplet
(Université Sorbonne Paris Nord)
Title
: Diffusive Hamilton-Jacobi equations and their singularities
Abstract: We consider the diffusive Hamilton-Jacobi equation $u_t-\Delta u=|\nabla u|^p$ with homogeneous Dirichlet boundary conditions, which plays an important role in stochastic optimal control theory and in certain models of surface growth (KPZ).

Despite its simplicity, in the superquadratic case p>2 it displays a variety of interesting and surprising behaviors and we will discuss two classes of phenomena:


- Gradient blow-up (GBU): localization of singularities on the boundary, single-point GBU, time rate of GBU, space and time-space profiles, Liouville type theorems and their applications;


- Continuation after GBU as a global viscosity solution: GBU with or without loss of boundary conditions (LBC), recovery of boundary conditions with or without regularization, GBU and LBC at multiple times.


In particular, in one space dimension, we will present the recently obtained, complete classification of all GBU and recovery rates.


This talk is based on a series of joint works in collaboration with A. Attouchi, R. Filippucci, Y. Li, N. Mizoguchi, A. Porretta, P. Pucci, Q. Zhang.


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  • Wednesday 2nd June at 15:00 (CET)

TBA