PDE Classification: Elliptic, Parabolic, and Hyperbolic

*please note that the left hand side of the parabolic equation should be differentiated with respect to time, not x.

In this video I discuss how PDEs are classified. The classifications include Elliptic, Parabolic, and Hyperbolic; this is an important topic because it provides intuition to the behavior of many heat and cfd problems. Along with introducing and describing the classes, I give a brief example of how a simple PDE can be classified. In a future video I will show how this procedure can be generalized to PDEs that rely on N variables.

[bansishah]

even slowed down, this is a very fast video !!!! content is awesome. But would prefer a slower version please !!

[madhavupadhyay]

Thank you for this explanation in a simple way

[comb]

Thank you very much for the simple explanation. There is one mistyping, dT/dx -> dT/dt in parabolic equation.

[AJ-etvf]

Thank you very much for this well-made lucid video. Very nice to get the gist of things immediately

[padaddadada]

Thank you for your video :

I think you made a mistake at 2:18 when writing the parabolic pde :
You replaced t by x in the left hand side of the equation.

[TheSumanth]

Should the Temperature T=TL be in the parabolic equation diagram example?

[fljia]

Agree with @Comb, at 2:08, the dT/dx should be dT/dt

[Cloud]

Can we classify PDEs of higher order ( 3rd or 4th) into elliptic, parabolic or hyperbolic by using any such formula?

[vshankarful]

** best to watch if you want to understand the physical significance in the classification of PDE..

[xbinarylol]

But elliptic PDE can also contain initial condition