Seminario

Otros Seminarios

SEMINARIO DOBLE DE ECUACIONES EN DERIVADAS PARCIALES - Linear Galerkin methods for a nonlinear time-fractional diffusion with nonsmooth data and applications to hydrology and climatology // Qualitative properties of solutions to -Delta_p u=f(u) in R^N_+

Ponente:  Łukasz Płociniczak, Wroclaw University of Science and Technology // Luigi Montoro, Università della Calabria ()
Fecha:  viernes 13 de mayo de 2022 - 13:00-14:30
Lugar:  Aula 520, Módulo 17, Departamento de Matemáticas, UAM
Online:  us06web.zoom.us/j/81991093838

Resumen:

"Linear Galerkin methods for a nonlinear time-fractional diffusion with nonsmooth data and applications to hydrology and climatology", Łukasz Płociniczak (Wroclaw University of Science and Technology)

Abstract: In this talk we will present some new results concerning construction and analysis of Galerkin numerical methods for the nonlocal in time quasilinear diffusion equation. These can be implemented both in the spectral or finite element setting. For the finite element case we will consider the case of the nonsmooth initial data and provide the error bounds assuming much weaker hypothesis than usually found in the literature.  The nonlinearity is dealt with extrapolation in time what results in a linear scheme. Lastly, we support the theory with numerical experiments.

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"Qualitative properties of solutions to $$-\Delta_pu=f(u)$$  in $$\mathbb R^N_+$$", Luigi Montoro (Università della Calabria)

Abstract: We consider weak distributional solutions to the equation $$-\Delta_pu=f(u)$$ in half-spaces under zero Dirichlet boundary condition. For a general class of regular changing-sign nonlinearities $$f$$, we prove that any positive solution is monotone increasing in the direction orthogonal to the boundary of the half-space $$\mathbb R^N_+$$.