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Title: Mixed problems for the Korteweg-de Vries equation

Journal Article · · Sbornik. Mathematics
 [1]
  1. Peoples Friendship University of Russia, Moscow (Russian Federation)

Results are established concerning the non-local solubility and wellposedness in various function spaces of the mixed problem for the Korteweg-de Vries equation u{sub t}+u{sub xxx}+au{sub x}+uu{sub x}=f(t,x) in the half-strip (0,T)x(-{infinity},0). Some a priori estimates of the solutions are obtained using a special solution J(t,x) of the linearized KdV equation of boundary potential type. Properties of J are studied which differ essentially as x{yields}+{infinity} or x{yields}-{infinity}. Application of this boundary potential enables us in particular to prove the existence of generalized solutions with non-regular boundary values.

OSTI ID:
21202860
Journal Information:
Sbornik. Mathematics, Vol. 190, Issue 6; Other Information: DOI: 10.1070/SM1999v190n06ABEH000408; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
Country of Publication:
United States
Language:
English

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