Toronto Math Forum
APM3462015S => APM346Home Assignments => Web Bonus Problems => Topic started by: Victor Ivrii on January 14, 2015, 09:20:14 AM

Solve
\begin{align}
&(t^2+1)u_{tt}+tu_tu_{xx}=0,\label{eq1}\\[3pt]
&u_{t=0}=0, \qquad u_t_{t=0}=1.\label{eq2}
\end{align}
Hint: Make a change of variables $x=\frac{1}{2}(\xi+\eta)$, $t=\sinh (\frac{1}{2}(\xi\eta))$ and calculate $u_\xi$, $u_\eta$, $u_{\xi\eta}$.

proï¼ŒI think there is a type error of the hint you provide, should x=(xi+eta)/2 instead of xi=(xi+eta)/2 ?
thx
Thanks, corrected. V.I.