Question: Solutions in the form of a function in pdsolve

I have a set of partial differential equations and one unknown function f(u,v) which must contain u*Heaviside(u) and v*Heaviside(v) multiplications. Heaviside(u) is the Heaviside step function for the parameter u and it is already defined in Maple.

The solution should come in terms of these multiplications, that is, u or v, or Heaviside(u) or Heaviside(v) cannot occur alone.

I tried a solution of the form,

f(u,v):=c1*u*Heaviside(u)+c2*v*Heaviside(v)+c3*u*v*Heaviside(u)*Heaviside(v)+c4*sqrt(u*Heaviside(u))+c5*sqrt(v*Heaviside(v))+c6*(u*Heaviside(u))^2+c7*(v*Heaviside(v))^2:

but the resulting system does not give me constant c1,c2...'s and it is not guaranteed that this form is the right one.

Therefore this way of solving the system is not efficient and I need to solve the system by "pdsolve" but I do not know how to define the form of the solution as these multiplications in pdsolve.

Any help or comment will be appreciated.