Coefficients for 2D PDE: Can you have a coefficient that is f(x(t),y(t),t) ?

Hi there, I am trying to solve the 2D heat equation with the PDE toolbox on a unit square. Using the information from the MATLAB instructions on "Specific 2D Scalar Coefficients in Functional Form", it is clear that we can create a coefficient that is a function of space and time, i.e. f(x,y,t).

My question is as follows: Is there a way to create a coefficient as f(x(t),y(t),t)? I would like the spatial distribution of my source term to be a circle with a time-varying radius. Is this possible? The output of the function apparently must be a row vector and not a matrix.

Thank you for your time, J

Answer 1

[Alan Weiss]

As far as I know, PDE Toolbox assumes that the geometry of the problem is fixed for all time. However, it might be possible to fake the problem by using a large geometry and writing functions that mimic having only part of the geometry used at any given time. But I do not know how you would implement boundary conditions that way.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation