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Task 2 (The Fisher-Kolmogorov equation) Consider the equation (complemented by an initial condition) u - Au = u(1 – u), u(0) = uo. Prove local existence and uniquenss of solutions using the ansatz u(t, z) = U(r + ct), (c > 0). Characterize the steady states of the equation and try to determine their (in)stability.

Task 2 (The Fisher-Kolmogorov equation) Consider the equation (complemented by an initial condition) u - Au = u(1 – u), u(0) = uo. Prove local existence and uniquenss of solutions using the ansatz u(t, z) = U(r + ct), (c > 0). Characterize the steady states of the equation and try to determine their (in)stability.

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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Task 2 (The Fisher-Kolmogorov equation) Consider the equation (complemented by an initial condition) u - Au = u(1 – u), u(0) s ug- Prove local existence and uniquenss of solutions using the ansatz u(t, r) = U(r + ct),. (c > 0). Characterize the steady states of the equation and try to determine their (in)stability.
Transcribed Image Text:Task 2 (The Fisher-Kolmogorov equation) Consider the equation (complemented by an initial condition) u - Au = u(1 – u), u(0) s ug- Prove local existence and uniquenss of solutions using the ansatz u(t, r) = U(r + ct),. (c > 0). Characterize the steady states of the equation and try to determine their (in)stability.
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