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5. Consider the system of first-order PDES –1 ut + Auz = 0, A = 3 x > 0, t>0 1 (a) Show that the characteristic velocities (i.e. the eigenvalues of A) are both real and positive. (b) Since the characteristic velocities are both positive, we require conditions on both components of u(x, t) along the initial line, t = 0 and x > 0, and along the boundary line, x = 0 and t > 0. Assume that f(x) u(x,0) = u(0, t) : Diagonalize the system and use the method of characteristics to find the solution for u(x,t).

5. Consider the system of first-order PDES –1 ut + Auz = 0, A = 3 x > 0, t>0 1 (a) Show that the characteristic velocities (i.e. the eigenvalues of A) are both real and positive. (b) Since the characteristic velocities are both positive, we require conditions on both components of u(x, t) along the initial line, t = 0 and x > 0, and along the boundary line, x = 0 and t > 0. Assume that f(x) u(x,0) = u(0, t) : Diagonalize the system and use the method of characteristics to find the solution for u(x,t).

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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5. Consider the system of first-order PDES -1 Ut + Au, = 0, A = 3 x > 0, t>0 1 (a) Show that the characteristic velocities (i.e. the eigenvalues of A) are both real and positive. (b) Since the characteristic velocities are both positive, we require conditions on both components of u(x, t) along the initial line, t = 0 and x > 0, and along the boundary line, x = 0 and t > 0. Assume that f(x) u(x, 0) = u(0, t) = Diagonalize the system and use the method of characteristics to find the solution for u(x, t).
Transcribed Image Text:5. Consider the system of first-order PDES -1 Ut + Au, = 0, A = 3 x > 0, t>0 1 (a) Show that the characteristic velocities (i.e. the eigenvalues of A) are both real and positive. (b) Since the characteristic velocities are both positive, we require conditions on both components of u(x, t) along the initial line, t = 0 and x > 0, and along the boundary line, x = 0 and t > 0. Assume that f(x) u(x, 0) = u(0, t) = Diagonalize the system and use the method of characteristics to find the solution for u(x, t).
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