Problem with periodicity conditions for a degenerating equation of mixed type |
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Authors: | K B Sabitov O G Sidorenko |
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Institution: | 1.Sterlitamak Division,Bashkir Academy of Sciences,Sterlitamak,Russia |
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Abstract: | For the equation K(t)u
xx
+ u
tt
− b
2
K(t)u = 0 in the rectangular domain D = “(x, t)‖ 0 < x < 1, −α < t < β”, where K(t) = (sgnt)|t|
m
, m > 0, and b > 0, α > 0, and β > 0 are given real numbers, we use the spectral method to obtain necessary and sufficient conditions for the unique solvability
of the boundary value problem u(0, t) = u(1, t), u
x
(0, t) = u
x
(1, t), −α ≤ t ≤ β, u(x, β) = φ(x), u(x,−α) = ψ(x), 0 ≤ x ≤ 1. |
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Keywords: | |
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