how can I solve this non linear partial differential equation mentioned below I have some initial & boundary condition

Answer 1

[Torsten]

Discretize the differential operators, include the boundary conditions and solve the resulting system of nonlinear equations for z'(i,j) (values of z' in (x'(i),y'(j))) using "fsolve".

[Rohan Singla]

can you explain in more detail.

[Torsten]

To get a more specific answer, you will have to provide more details about your problem.

What is kappa^i ? Is it a constant throughout the domain where you want to solve your PDE ? What is the domain where you want to solve the PDE ? What are the boundary conditions ?

Maybe you could also explain in which context this PDE appears.

[Rohan Singla]

can you share your e-maild id? i can discuss and share whole problem there?

[Torsten]

No, sorry. I only communicate via the forum.

Answer 2

[Rohan Singla]

I need to obtain profile

k^i =constant value of =6.54×10-3 μm -1

this is the boundary condition

here x',y',z' are the coordinates in x,y,z plane

and (d = 10 μm, l = 30 μm, h = 25 μm)

and these are intial condition

thanks alot

[Torsten]

Above, you define 4 circles. I can't decipher on which circle you want to solve the PDE and what boundary condition you want to impose for z' on the circumpherence.