## MAP-PDMA

**Eurica Henriques**

*CMAT - University of Minho*

**Abstract ::**

Differential equations govern several phenomena and their study gives rise to some answers and several other questions. In this seminar we go on a tour starting at Newton’s cooling law (an ordinary differential equation), stoping briefly at some well known partial differential equations (pde) and ending on a doubly nonlinear pde. We will present recent results concerning regularity aspects of the weak solutions to the doubly nonlinear pde

\begin{displaymath}

u_t-\textrm{div} \big(|u|^{m-1} |Du|^{p-2} Du\big)=0 , \qquad p>1

\end{displaymath}

**References**

[1] S. Fornaro, E. Henriques and V. Vespri, Regularity results for a class of doubly nonlinear very singular parabolic equations, Nonlinear Anal., 205 (112213), 30 pp, 2021.

[2] S. Fornaro, E. Henriques and V. Vespri, Stability to a class of doubly nonlinear very singular parabolic equations, manuscripta math, 2021 https://doi.org/10.1007/s00229-021-01302-w

[3] S. Fornaro, E. Henriques and V. Vespri, Harnack type inequalities for the parabolic logarithmic p-Laplacian equation title of the paper, Le Matematiche, 75, 277–311, 2020.

**Zoom link:** https://videoconf-colibri.zoom.us/j/86389857315

Seminar for the Doctoral Program in Applied Mathematics (MAP-PDMA Seminar)