I noticed these erosion patterns in the sand formed by waves lapping the shore. They reminded me of Turing patterns. #SouthHaven #Michigan #LakeMichigan #PartialDifferentialEquations

We congratulate Prof #LuisCaffarelli 🥳

The #WorldMathAbelPrize 2023 was given to Luis Caffarelli, a former member of the Scientific Advisory Board of the
@ESIVienna. He has been making important contribution to the subject #nonlinear #PartialDifferentialEquations.

Dive into his work here: https://abelprize.no
https://esi.ac.at/news/n38

@univienna
#Abel2023

Photo by © by Nolan Zunk

Ah, the remembered romance of
∂︎f(x,y)/∂︎x + ∂︎f(x,y)/∂︎y = 0
and all that!
#AbelPrize #PartialDifferentialEquations #Maths https://www.theguardian.com/science/2023/mar/22/the-messi-of-maths-argentinian-luis-caffarelli-wins-abel-prize

Three edges of an insulated metal plate are kept constant at 0 degrees #Celsius while a fourth edge is held at 100 degrees. 🌡

The #LaplaceEquation in 2 spatial dimensions gives the steady-state temperature distribution at all points within the plate under these conditions. Blue corresponds to cool temperatures, red corresponds to hot temperatures, and shades of green and yellow correspond to intermediate temperatures.
#PartialDifferentialEquations #HeatEquation #Elliptic #Math

The #HeatEquation in 2 spatial dimensions. Three edges of an (insulated!) rectangular plate are held at 0 degrees #Celsius, while the fourth edge is held at 100 degrees.🌡 The plate is initially 0 degrees throughout.
The #LaplaceEquation (depicted below the animated time-dependent solution) gives the steady-state temperature distribution within the plate, which the time-dependent solution approaches. 🍿🥤
#PartialDifferentialEquations

#PartialDifferentialEquations in 2 spatial dimensions.