Mixed problems for the Korteweg-de Vries equation
Journal Article
·
· Sbornik. Mathematics
- 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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