Problem 1. Let u(t, x) be a bounded solution to the following problem for the heat equation Ut = Uxx, (t, x) = (0, t) x R u(0, x) = (x). Assume that the initial data (x) = C(R) satisfies lim p(x)=b, x48 Compute the limit of u(t, x) as t → ∞, x ER. lim (x) = c. x118

Problem 1. Let u(t, x) be a bounded solution to the following problem for the heat equation Ut = Uxx, (t, x) = (0, t) x R u(0, x) = (x). Assume that the initial data (x) = C(R) satisfies lim p(x)=b, x48 Compute the limit of u(t, x) as t → ∞, x ER. lim (x) = c. x118

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.

Chapter14: Discrete Dynamical Systems

Section14.3: Determining Stability

Problem 13E: Repeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii...

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Question

Problem 1. Let u(t, x) be a bounded solution to the following problem for the heat equation
Ut = Uxx, (t, x) € (0,t) x R
u(0, x) = (x).
Assume that the initial data (x) = C(R) satisfies
lim p(x)=b,
x48
lim p(x) = c.
X118
Compute the limit of u(t, x) as t → ∞, x € R.

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