For a general dynamic system: dXi/dt = Fi(X1, X2,...,Xn), i=1,...,n,(adsbygoogle = window.adsbygoogle || []).push({});

Q.1

do you have some ideas of the existence conditions of following PDE:

a) (grad U, grad U + F) = 0 in n-dimension domain, (,) is inner product;

b) U >=0

Does it need a first type or second type of boundary condition?

Q.2

If solution does exist, how to solve it numerically?

- I tried to write in differential equation in matrix format, then apply Newton method. It is very difficult to have a converge scheme.

A more detailed simple example is attached to explain the solution that I tried.

Many thanks for your ideas or comments

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Solution for a nonlinear PDE

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**