I'm trying to solve a non-linear time-dependent diffusion equation to find R(x,t). To do so, I'm positing that :(adsbygoogle = window.adsbygoogle || []).push({});

R(x,t)=[itex]\sum^{J}_{1}[/itex]X[itex]_{i}[/itex](x)T[itex]_{i}[/itex](t)

which allows me to arrive at something that looks like :

dT[itex]_{i}[/itex]/dt=A[itex]_{i}[/itex]T[itex]_{i}[/itex](t)-B*T[itex]_{i}[/itex](t)[itex]^{2}[/itex]

The problem I'm having, through sheer lack of knowledge, is ascribing initial conditions to T[itex]_{i}[/itex](t).

I know that R(x,0) = 1. Taking the case where J = 3, for example, can I simply say that T[itex]_{i}[/itex](0) = 1/3? If not, is there a way to determine the initial conditions for each T[itex]_{i}[/itex](t), given that I know that they need to sum to 1?

Thank you kindly for any help.

-ryan

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# Applying initial conditions to functions that are part of an Eigenfunction Expansion

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