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Unformatted text preview: the rod). (b) In each case above, nd the solution of the problem as an innite series. Express the coecients as ratios of integrals, but do not attempt to evaluate them. The series and integrals will involve the eigenvalues from (a), so you wont be able to be too specic. (c) Discuss the behavior of u ( x, t ) as t . You should nd, in the various cases of (a), that (i) u ( x, t ) approaches zero as t ; (ii) u ( x, t ) approaches a non-zero steady state as t ; (iii) u ( x, t ) becomes innite (blows up) as t . (d) What is the physical interpretation of the boundary condition at x = L when > 1, and why, on physical grounds, does the solution blow up in that case?...
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This note was uploaded on 12/15/2009 for the course MATH 527 taught by Professor Staff during the Fall '08 term at Rutgers.
- Fall '08