Recent content by fery

Yes F(f) is a real number, as I said it is a mapping in R, the reason I put x in F(f,x) is that sometimes x is explicitly in the functional. for example it is possible to write int((f^2+x^2),a,b) as a functional http://mathworld.wolfram.com/Euler-LagrangeDifferentialEquation.html The inclusion...

All true but F(x,f(x)) is a functional not a function, which is mapping of a function to R. For minimization of the functional Euler-Lagrange is the conventional method, but when there is constraint (int(G(t,f(t),a,b)=M) I am not sure what should I do. Farshad

I am working on a functional and I need to find its minimum, the conventional procedure is to use Lagrange-Euler method and find the minimum state of the function, but if I need to impose a constraint to the function, I don't know what I need to do J=int(F(t, f(t), a, b)) minimize(f) and...

If you are asking me, I don't think these functions represent the general solution of the equation. And they are not orthogonal so if they would be the general solution, we would never be able to find particular solution for them.

Thanks you, I am not quite sure about the second type, can you fix the Parenthesis.

Sure, P = P(x,y,t), Laplacian = d/dx2 + d/dy2, As I said this nonlinear equation represents diffusion of capillary pressure in porous media.

Hi I have a nonlinear equation for diffusion of multiphase fluids in porous media, and it is like 1/2(Laplacian(P^2)+d(p)/dy=d(p)/dt I couldn't find any analytical or semianalytical solution for this equation, do you have any idea?