Solve multiple integrals qith Newton-Cotes formulas

Hi!! I'm trying to compute a biological model and one of the parts of it consists in a multiple integral function I am not being able to solve. I would highly appreciate if someone could guide me or help me in how to do it. The model equation is

and

Where pm= 0.06; Rmax = 70cm and u is the model function. I am not sure of how to solve it cause the general model includes the p function and the p function includes the u fuinction.

Thank you in advance

[Torsten]

Do you have the complete vector of u-values over the [0,Rmax] x [0,rho_m] available in each time step ?

Where do you need rho_a(t) ? Only for postprocessing or within the model function ?

[Ana Gabriela Guedes]

No, I don't. That is why I am not usre of how to do it since I cant set the initial and boundarie conditions as I usually do when solving differential equations...

According to the paper I am following, rho is the distribution of the proliferation rates and is reflected in the average proliferation rate, rho_a(t).

[Torsten]

If you don't have the complete u-vector available in each time step, you won't be able to solve the above equation.

It seems you have a 2d in space PDE (r and rho as independent variables). Did you plan to use MATLAB's PDE toolbox to solve ?