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Problem: Consider the heat boundary value problem Ә ?x ди Ət u(0, t) + a ди Әх (1 + a)u(L,t) + ди ?х (0, t) = 0, u(x, 0) = g(x), ди ət (x,0) = 0. - xu, 00, ди Әх -(L,t) = 0, a) Use separation of variables and show that the corresponding Sturm- Liouville problem is regular b) Determine the values of a for which the eigenvalues are nonnegative.

Problem: Consider the heat boundary value problem Ә ?x ди Ət u(0, t) + a ди Әх (1 + a)u(L,t) + ди ?х (0, t) = 0, u(x, 0) = g(x), ди ət (x,0) = 0. - xu, 00, ди Әх -(L,t) = 0, a) Use separation of variables and show that the corresponding Sturm- Liouville problem is regular b) Determine the values of a for which the eigenvalues are nonnegative.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Problem: Consider the heat boundary value problem Ә ди -х техн Ax Ju Әx ди Ət = eit u(0, t) + a (0, t) = 0, (1 + a)u(L,t) + u(x, 0) = g(x), ди (x,0) = 0. Ət - xu, 0<x<L, t> 0, ди Әх (L,t) = 0, a) Use separation of variables and show that the corresponding Sturm- Liouville problem is regular b) Determine the values of a for which the eigenvalues are nonnegative.
Transcribed Image Text:Problem: Consider the heat boundary value problem Ә ди -х техн Ax Ju Әx ди Ət = eit u(0, t) + a (0, t) = 0, (1 + a)u(L,t) + u(x, 0) = g(x), ди (x,0) = 0. Ət - xu, 0<x<L, t> 0, ди Әх (L,t) = 0, a) Use separation of variables and show that the corresponding Sturm- Liouville problem is regular b) Determine the values of a for which the eigenvalues are nonnegative.
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