homework3

# homework3 - 1.6.1(b What is the type of the following...

This preview shows page 1. Sign up to view the full content.

Problem 1 (not from the textbook). Solve the initial value problem: u x + 2 xu y = 2 xu, u (0 ,y ) = y 2 by two di erent methods (using parametrization of the characteristic curve such as γ ( s ) = ( x ( s ) ,y ( s )) and such as γ ( x ) = ( x,y ( x )) . Hint - see pdf notes for the second week lectures ) Sketch the initial value line and some characteristics. Find the domain of well-posedness of the problem.
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1.6.1 (b) What is the type of the following equation ? 9 u xx + 6 u xy + u yy + u x = 0 1.6.2 Find the regions in the xy plane where the equation (1 + x ) u xx + 2 xy u xy-y 2 u yy = 0 is elliptic, hyperbolic, or parabolic. Sketch them. 2.1.10 Solve u xx + u xt-20 u tt = 0 , u ( x, 0) = φ ( x ) , u t ( x, 0) = ψ ( x ) . 1...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern