Partial Differential Equations question:
A sensor at position x = 1 monitors the concentration of the pollutant u(t,1) as a function of t for t= 0. Assuming the pollutant is transported (i.e. the transport equation is governing its movement) with wave speed c = 3, at what positions x can you determine the initial concentration u(0,x)?

I have worked on this a bit, but don't know what to do. A complete explanation would be appreciated.

Question

Partial Differential Equations question:
A sensor at position x = 1 monitors the concentration of the pollutant u(t,1) as a function of t for t>= 0. Assuming the pollutant is transported (i.e. the transport equation is governing its movement) with wave speed c = 3, at what positions x can you determine the initial concentration u(0,x)?

I have worked on this a bit, but don't know what to do. A complete explanation would be appreciated.

anonymous · Answer

See page 11 of http://www.math.ucsb.edu/~grigoryan/124A.pdf $$0

anonymous · Answer

Thank you for the reference, I'll get busy digging

anonymous · Answer

I'll have to look at the notes a bit longer because I don't remember our teacher mentioning solving stuff by method of characteristics... :(