This preview shows page 1. Sign up to view the full content.
Unformatted text preview: with the base [0 ,l ] . Problem 5 (challenging problem) Use the energy method to prove that for t big enough 1 2 Z + - ( u t ) 2 dx = 1 2 Z + - ( u x ) 2 dx (equipartition of kinetic and potential energies for large times) if u xx-u tt = 0 , u ( x, 0) = ( x ) , u t ( x, 0) = ( x ) where ( x ) and ( x ) have compact support. 1...
View Full Document
- Fall '11