hw9 - Math 425, Spring 2011 Jerry L. Kazdan Problem Set 9...

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 425, Spring 2011 Jerry L. Kazdan Problem Set 9 DUE: Thursday April 7 [ Late papers will be accepted until 1:00 PM Friday ]. 1. a) In a bounded region R n , let u ( x , t ) satisfy the modified heat equation u t = u + cu , where c is a constant , (1) as well as the initial and boundary conditions u ( x , ) = f ( x ) , in with u ( x , t ) = 0 for x , t . (2) Let u ( x , t ) = v ( x , t ) e t . Show that by picking the constant cleverly, v satisfies equation (1) with c = 0 as well as (2). Moral: one can easily reduce understanding equations (1)-(2) to the special case c = 0. b) Generalize this to u t + a ( t ) u = u where a ( t ) is any continuous function by seeking u ( x , t ) = ( t ) v ( x , t ) and picking the function ( t ) cleverly, 2. In a bounded region R n , use the maximum principle to prove a uniqueness theorem for solutions u ( x , t ) of the inhomogeneous equation u t- u = F ( x , t ) in with u ( x , ) = f ( x ) , in...
View Full Document

Page1 / 2

hw9 - Math 425, Spring 2011 Jerry L. Kazdan Problem Set 9...

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