Problem 2. Let be a bounded domain. Let u be a C² solution to the heat equation(dt − A)u = fin R+ x nu(0, x) = uo(x)in Ωu(t, x) = 0 in R+ × anAssume that |uo| ≤ A and |f|≤ B. Show that|u(t, x)| ≤ A+tB

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Answered: Problem 2. Let be a bounded domain. Let…

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 2. Let be a bounded domain. Let u be a C2 solution to the heat equation in R+ x N (dt - A) u = f u(0, x) = u₁(x) u(t, x) = 0 in R+ × an in Ω { Assume that |uo| ≤ A and |f|≤ B. Show that |u(t, x)| ≤ A+tB