What are the applications of non-linear PDEs in physics and engineering?

[DevacDave]

Hello Everybody!

I'm an applied mathematics researcher who found out about this website through the courtesy of one of my awesome students. My main degree is in physics, but afterwards I have been leaning more and more in the direction of mathematics and programming. Most of my work orbits around non-linear PDE that pop-up in physics and engineering. As far as hobbies go I think that I have too many of them to list, but I should mention that bashing on people who think that Mathematica will replace the need for mathematicians and mathematics education is among my cherished pleasures. I do like and use Mathematica, it's just the above mindset that bugs me. Other ones (interests and hobbies) would be condensed matter physics and DIY electronics projects.

English is not my primary language, but I think that I am far from being incomprehensible ;).

 

[Greg Bernhardt]

Welcome to PF!

 

[S.G. Janssens]

I should mention that bashing on people who think that Mathematica will replace the need for mathematicians and mathematics education is among my cherished pleasures. I do like and use Mathematica, it's just the above mindset that bugs me.

I like it when people cherish their annoyances, especially when they are right. Welcome here!

EDIT: Maybe you can briefly tell a bit more about your research? Is there a particular kind of PDE (a particular class of problems) that you are interested in?

 

[Silicon Waffle]

I like it when people cherish their annoyances, especially when they are right. Welcome here!

EDIT: Maybe you can briefly tell a bit more about your research? Is there a particular kind of PDE (a particular class of problems) that you are interested in?

Polar bear! you have a good like!

 

[DevacDave]

I like it when people cherish their annoyances, especially when they are right. Welcome here!

EDIT: Maybe you can briefly tell a bit more about your research? Is there a particular kind of PDE (a particular class of problems) that you are interested in?

I'm definitely guilty on spending too much of my free time on giving a shot with Navier-Stokes Equation ;). But my fairly recent research in shallow water waves for modelling movement of sediments and shore erosion made me look closer and closer in that direction.

 

[S.G. Janssens]

I'm definitely guilty on spending too much of my free time on giving a shot with Navier-Stokes Equation ;).

This must be a beautiful topic, mathematically profound while simultaneously very close to direct applications. It is certainly on my long-time list of subjects that deserve much closer studying.