pdepe when source term is zero, the total mass still increase over time

Hey guys,

I'm trying to solve a simple 1D partial differential equation, but I run into some problem that I can't figure out how to solve it. I don't have a lot of math background.

So, the equation is:

with no-flux boundary condition.

To use pdexpde, for pdex1pde I have:

c = 1;
f = -strain*u*cos(x)*sin(x);
s = (1-u)*kdiss;

where kdiss is in original function, and strain is ξ in original function.

for initial condition pdex1ic, I started with steady state condition, which is:

u0 = 1;

for boundary condition pdex1bc, I used no-flux boundary condition:

pl = 0;
ql = 1;
pr = 0;
qr = 1;

I started with the steady state condition, so I feel like over time the total mass should stay constant. However, increase gradually overtime. The closer strain and kdiss are, the more dramatic this problem becomes. For a rather extreme case, when I turn off source term, such that:

c = 1;
f = -strain*u*cos(x)*sin(x);
s = 0;

Even in this case, the still increase gradually.

I am wondering if anyone could help me with this problem? Thanks a lot for your time and effort!

Best,

[Bill Greene]

It can be challenging to obtain solutions with pdepe when the flux term has no dependence on . I suggest you provide more details about the specific values of your constants, the mesh you are using, and the time scale of the problem.