Solve first order PDEs system

Hi all
i have some troubles in solving this PDE system, i don't know which is the most effective method. I have searched a lot online but i haven't found methods that involve a system of first order equations where each one is derived in time and space. The unknowns are Tt, Pt and M, each one is a functions of x and t. All the other terms in the equations are constant.
Thank you

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They are too complicated for this community
Do you know any software that can do it then?

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R2019a

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2020-5-20

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