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Does anyone know if there are solutions to the following PDE

$$u_t + u_x = f(x,t)$$

If not in a general context, what if ##f(x,t) = \delta(x-at)/(x-at)##? Please let me know if you have any information.

Method of characteristics?

$$u_t + u_x = f(x,t)$$

If not in a general context, what if ##f(x,t) = \delta(x-at)/(x-at)##? Please let me know if you have any information.

Method of characteristics?

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