1. This question studies the stability of the solution of the heat equation. Let D be abounded domain in R3 and let Qrinitial-boundary problems of the heat equation respectively:= D × (0,T. Assume that u1 and u2 solve the(u1)t = kA(u1) +hU1 = f1(u1)|t-0 = 91in Qron ðD × [0,T]|(2); = kA(u2) + hU2 = f2(u2)-0 =in QTon ôD × [0, T)in D92in DAssume thatmax fi- f2 +max |g1 – 92| < E.aD×[0,T]Show thatmax |u1 – u2| < E.QT

Let D be the bounded domain in ℝ3 and let QT=D×(0,T ]. u1t=k∆u1+hin QTu1=f1on ∂D×(0,T]u1t=0=g1in…

1. This question studies the stability of the solution of the heat equation. Let D be a bounded domain in R3 and let Qr = D × (0,T|. Assume that u1 and uz solve the initial-boundary problems of the heat equation respectively: (u1); = kA(u1) + h U1 = fi (u1)|-0 in Qr on ðD × [0,T|| (u2): = kA(u2) +h U2 = f2 (u2)|-0 in QT on ƏD × [0,T] = 9i in D = 92 in D Assume that max fi - f2 +max |g1 – 92| < E. aDx[0,T] D Show that max u1 – u2| < E. QT

1. This question studies the stability of the solution of the heat equation. Let D be a bounded domain in R3 and let Qr = D × (0,T|. Assume that u1 and uz solve the initial-boundary problems of the heat equation respectively: (u1); = kA(u1) + h U1 = fi (u1)|-0 in Qr on ðD × [0,T|| (u2): = kA(u2) +h U2 = f2 (u2)|-0 in QT on ƏD × [0,T] = 9i in D = 92 in D Assume that max fi - f2 +max |g1 – 92| < E. aDx[0,T] D Show that max u1 – u2| < E. QT

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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