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Question: Solving sets of PDE perturbatively?

Question:Solving sets of PDE perturbatively?

Jamie128 165
pde pdsolve differential-equations
April 25 2023
1

I dont know if this is a well formulated question but if I had a set of PDES that have a constant appearing in them (say alpha), would there be a way to solve for the PDE such that the right had side is not zero but just has higher order order terms (say alpha^3 and higher).

For example consider (the random set of equations)
 

eq1 := alpha*diff(f(t, r), r,r) + diff(g(t, r), t) + alpha*g(t, r) = 0;
           

eq2 := alpha*diff(g(t, r), r) + diff(f(t, r), t,t) + f(t, r) = 0;

Is there a way to solve for the system of pde such that the right hand side is only terms of order alpha^3 and higher?
 
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