How can I solve this coupled partial differential equation?

Where CMG, X and xan are measured values, the relationship between DMG and xan is shown in the figure above, and a, R and T are constants. How to solve t?

[John D'Errico]

Your second equation is not an equation of equality at all, nor is it a differential equation. It is merely a description of a region where any solution set must lie. "Numbers" like -6.06+/-1.10 are not constants, just statements of an interval of complete uncertainty.

Not only that, but you differentiate C_Mg in there, but you tell us it is a measured value. Worse, you also tell us that X_An is a measured value.

I'm sorry, but it is not at all clear what you have here, and what you hope to solve for, nor even why you think this is a differential equation you can solve.

[dpb]

"...you differentiate C_Mg in there, but you tell us it is a measured value. Worse, you also tell us that X_An is a measured value. "

Mayhaps there is a set of measurements versus x, not just a single point so either a numerical derivative or an interpolated form could be created?

[Torsten]

You have 2 equations, but 3 unknowns: C_Mg, X_An and D_mg. Thus besides the strange region-like definition of D_mg, you miss a third equation (for X_An).

[Walter Roberson]

@Torsten

They said that xan is a measured value.

... which doesn't tell us anything about the partial derivative of xan with respect to x.

[Torsten]

@Walter Roberson

Ah - I only had eyes for the equations. But if there are measurements for all variables, what remains to be solved ? Maybe the measured concentrations are to be reproduced by simulation.