Note on a maximum principle and a uniqueness theorem for an elliptic-hyperbolic equation
1956 ◽
Vol 236
(1204)
◽
pp. 141-144
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Keyword(s):
Type K
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A maximum principle is proved for the function ψ = J [ — 2u x u y dx + (Ku 2 x — u 2 y ) dy], where u is a solution of the equation of mixed type K(y)u xx + u yy = 0 with K(y) ≷ 0 for y ≷ 0. The proof rests in showing that iff satisfies an elliptic equation for y > 0 and that it is a non-decreasing function of y for y ⩽ 0. This maximum principle leads to a uniqueness theorem for the appropriate analogue to the Dirichlet problem for mixed equations under some conditions on the shape of the boundary curve. Very weak restrictions are imposed on K(y).
Keyword(s):
2020 ◽
Vol 41
(11)
◽
pp. 2155-2167
Keyword(s):
2014 ◽
Vol 32
(5_6)
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pp. 721-736
1963 ◽
Vol 61
(1)
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pp. 371-377
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1981 ◽
Vol 39
(1)
◽
pp. 107-123
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1983 ◽
Vol 5
(1)
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pp. 346-355