Unformatted text preview: n = 3, then there exists a constant C such that | u ( x ,t ) | < C 1 + t for x ∈ R 3 , t > b. Show that for n = 3, at a Fxed point x outside the support of φ and ψ , there exists an earliest impact time t i > 0 that depends on x so that u ( x ,t ) = 0 , for 0 ≤ t < t i , and that there also exists a Fnal impact time t f > t i so that for t > t f , u ( x ,t ) = 0. c. Show that for n = 2, for x outside the support of ψ and φ , there exists an initial impact time t i > 0 depending on x but no Fnal Fnal impact time t f . Hint: Examine carefully the consequences of Poisson and Kircho± formula. 1...
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This note was uploaded on 07/26/2011 for the course MATH 716 taught by Professor Tanveer,s during the Spring '08 term at Ohio State.
- Spring '08