# Hyperbolic Partial differential equation

I have the following problem: $$u_{t}(x,t)+a(x,t)u_{x}(x,t)-f(x,t)=0\\ \ u(x,0)=0, \\$$

How to solve this equation? Thank you.

• Look for a characteristic line. – mookid Mar 1 '14 at 8:57
• – Mhenni Benghorbal Mar 5 '14 at 5:57