Timeline for Analytic solution of a system of linear, hyperbolic, first order, partial differential equations

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Jun 18, 2014 at 14:59	comment	added	Robert Israel		If, for example, your initial data at $t=0$ are in $L^2$, you can do a Fourier transform, and then you're looking at a "generalized linear combination" of solutions of the form $u(x,y,t) = \exp(\alpha x + \beta y) v(t)$ for imaginary $\alpha$ and $\beta$.
Jun 18, 2014 at 14:41	comment	added	FraSchelle		Thanks again. I verified and it works pretty well. So in fact a separation of variable is sufficient to resolve this problem. Is there a way to prove that we exhaust the solutions by this Ansatz you proposed ? Thanks again for your clear and insightful answer.
Jun 18, 2014 at 14:31	vote	accept	FraSchelle
Jun 18, 2014 at 10:30	comment	added	FraSchelle		@RobertIsreal Thanks so much. I'll try your ansatz and the associated method asap, and tell you if it works (I guess it is). Still, is there references about that, or is it mathematical skills and intuitions acquired along years? Thanks again.
Jun 18, 2014 at 5:45	history	edited	Robert Israel	CC BY-SA 3.0	added 160 characters in body
Jun 17, 2014 at 23:48	history	edited	Robert Israel	CC BY-SA 3.0	added 340 characters in body
Jun 17, 2014 at 23:41	history	edited	Robert Israel	CC BY-SA 3.0	added 340 characters in body
Jun 17, 2014 at 23:28	history	answered	Robert Israel	CC BY-SA 3.0