0

I am really new to Mathematica, so please bear with me if I ask any relatively easy questions. I am trying to model/solve a specific instance of a 1D diffusion equation in which I have a nonlinear Neumann boundary condition at x=1 (length of unit 1). My equations that I have are:

D[u[x,t],t] == D[u[x,t], x, x] for the general diffusion equation;

D[u[1,t],x] == 10 - Log[u[1, t]] for a flux at boundary x=1 that begins at 10 and decreases as a function of Log of concentration at the boundary;

D[u[0,t],x] == 0 for a no flux boundary at x=0;

u[x,0] == 0 for an initial concentration of 0 everywhere in the rod.

What I am trying to see occur is a function where the heat spreads across the rod and smoothes out across the rod to a steady-state/equilibrium; additionally, the goal is to have the flux approach zero and remain at zero (which represents the difference in chemical potentials between the domain and an external source approaching zero).

I have tried to use DSolve to find a symbolic solution for the boundaries and equations, but it returns "General solution is not available for the given linear partial differential equation. Trying to build a special solution" as expected.

I wanted it to be more manipulative (with x=L as a boundary instead of x=1 and other coefficients), but a friend recommended using NDSolve. This has been even more confusing and has lead to more errors and useless material.

Am I going about this problem the correct way in which functions I am using? What do you guys recommend that I do instead? If you would like more detail, please let me know! I need all the help I can get.enter image description here

user21
  • 39,710
  • 8
  • 110
  • 167
Henoc Zinga
  • 13
  • 3
  • 2
    What do you guys recommend that I do instead? try NDSolve instead. – Nasser Jul 04 '21 at 08:00
  • Welcome to Mathematica.SE! I hope you will become a regular contributor. To get started, 1) take the introductory [tour] now, 2) when you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge, 3) remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign, and 4) give help too, by answering questions in your areas of expertise. – bbgodfrey Jul 04 '21 at 17:08
  • 3
    Please include your code in Mathematica format, not an image. so that readers can run your code without retyping it. – bbgodfrey Jul 04 '21 at 17:10

0 Answers0