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I'm looking for a solution to

u_t + A u_x + B (u - f) = 0

where f is a given function linear in x and constant in t.

u(x,0) = f(x)

u(0,t) = f(0)

A and B constant. Does this equation have a name? It's almost the inviscid Burger, but has the damping term (B u) and force term (B f).

Also, any ideas on a solution? I've tried method of characteristics but I trip over the third term and/or the boundary conditions

Regards, John

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# 1D advection with damping/forcing

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