Transform a PDE with Laplace transform

Hello, I have a problematic PDE that I am not sure can be solved at all, however I thought it could be transformed to another form by Laplace method.

The equation is:

a*b/u*v = 0

where a and b are arbitrary constants, and u an v are two unknown functions. To me it appears this has no solution, however I would like to ask if anyone has some suggestions.

Thanks