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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

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

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.3: Euler's Method
Problem 1YT: Use Eulers method to approximate the solution of dydtx2y2=1, with y(0)=2, for [0,1]. Use h=0.2.
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Problem 2. Let be a bounded domain. Let u be a C² solution to the heat equation (dt − A)u = f in R+ x n u(0, x) = uo(x) in Ω u(t, x) = 0 in R+ × an Assume that |uo| ≤ A and |f|≤ B. Show that |u(t, x)| ≤ A+tB
Transcribed Image Text:Problem 2. Let be a bounded domain. Let u be a C² solution to the heat equation (dt − A)u = f in R+ x n u(0, x) = uo(x) in Ω u(t, x) = 0 in R+ × an Assume that |uo| ≤ A and |f|≤ B. Show that |u(t, x)| ≤ A+tB
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