Question

Consider $U_x + U_y = 0$ with the initial condition $\ U(x,0) = \begin{cases} 0 & x < 0 \\ U_0(x-1) & x > 0 \end{cases}$ Where $U_0 > 0$. There is a weak solution $U(x,y)$ that has a jump discontinuity along a curve $x = \xi(y)$. Find this curve and describe the weak solution.

          Consider $U_x + U_y = 0$ with the initial condition
$\ U(x,0) = \begin{cases} 0 & x < 0 \\ U_0(x-1) & x > 0 \end{cases}$
Where $U_0 > 0$. There is a weak solution $U(x,y)$ that has a jump discontinuity along a curve $x = \xi(y)$. Find this curve and describe the weak solution.

Consider Ux + Uy = 0 with the initial condition
U(x,0) = 0 x < 0
U0(x-1) x > 0
Where U0 > 0. There is a weak solution U(x,y) that has a jump discontinuity along a curve x = ξ(y). Find this curve and describe the weak solution.

Added by Jose B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Thanks for your feedback!

Consider the initial equation UVx+Vy=O. Consider vot.pvo? XLO. V(x0=x>0. U.x-1 v01fh1os is a weak Where Uo >oThere jvmp disco+inui+y that has V(x,y) x=y)Find this a curve the-weak vatrios ad describe Curve.