Question

4. Solve the Dirichlet problem in an infinite strip: uxx + Uyy 0 <у<b, u(x, 0) — S(x), и(х, b) — g(x). (Hint: First do the case The case g 0 reduces to this one general case is obtained by superposition.) 0 for xe R and f = 0 by the substitution y — b - у, and the = Answer: sin(7y/b)g(t)dt cosh z(x - 1)/b) + сos(лу/b)] sin(zy/b)f(t)dt cosh(z (x — 1)/b] - cos(пу/b) 1 4. 2b

Solve the Dirichlet problem in an infinite strip uxx + uyy=0 for x ϵ R and 0 <y <b , u(x,0)=f(x) , u(x,b)=g(x). (Hint: first do the case f=0. The case g=0 reduces to this one by the substitution y→ b-y , and the case general is obtained by superposition)

Answer 1

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