220-HW2 - MATH 220: PROBLEM SET 2 DUE THURSDAY, OCTOBER 8,...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH 220: PROBLEM SET 2 DUE THURSDAY, OCTOBER 8, 2009 Problem 1. Show that the only solution u D ( R ) of u = 0 is u = c , c a constant function. Hint: u = 0 means that u ( ) = 0 for all C c ( R ). You need to show that there is a constant c such that u ( ) = integraltext c dx for all C c ( R ). To do so, consider when C c ( R ) is of the form = , C c ( R ), paying particular attention to the issue of compact supports. Then write an arbitrary as a linear combination of a fixed C c ( R ) and the derivative of some C c ( R ). Problem 2. Consider the PDE au x + u y = 0 . We already know that the C 1 solutions are of the form u ( x, y ) = f ( x- ay ), f C 1 ( R ). (1) Show that if f is merely piecewise continuous (or if you wish locally inte- grable), then the so defined u still solves the PDE in the sense of distribu- tions....
View Full Document

Page1 / 2

220-HW2 - MATH 220: PROBLEM SET 2 DUE THURSDAY, OCTOBER 8,...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online