(b) Find the solution of Laplace's equation outside a unit circle a?u 1 du 1 a2u 0, (r>1,0<0 < 2x), %3D subject to the boundary condition u(1,0) = 2 sin 30, having in mind the requirements that the solution must satisfy in an unbounded domain.
(b) Find the solution of Laplace's equation outside a unit circle a?u 1 du 1 a2u 0, (r>1,0<0 < 2x), %3D subject to the boundary condition u(1,0) = 2 sin 30, having in mind the requirements that the solution must satisfy in an unbounded domain.
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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part B
Transcribed Image Text:1.
(a) Consider the equation
e'ux+2ayuy +2eu,- sin(y) u =0,
where a is a real constant. Determine the value(s) of a when this equation is elliptic
everywhere in the xy-plane, in which case find the canonical variables and reduce the
equation to its canonical form.
(b) Find the solution of Laplace's equation outside a unit circle
a?u 1 du
0,
(r>1,0<0 < 2x),
zee e
subject to the boundary condition
u(1,0) = 2 sin 30,
having in mind the requirements that the solution must satisfy in an unbounded domain.
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