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On the Korteweg-de Vries equation
Existence, uniqueness, and continuous dependence on the initial data are proved for the local (in time) solution of the (generalized) Korteweg-de Vries equation on the real line, with the initial function ϕ in the Sobolev space of order s>3/2 and the solution u(t) staying in the same space, s=∞ being included For the proper KdV equation, existence of global solutions follows if s≥2. The proof is based on the theory of abstract quasilinear evolution equations developed elsewhere.
89-99
2019-04-11T09:10
http://link.springer.com/10.1007/BF01647967
research_article
1979-01-01
1979-01
https://scigraph.springernature.com/explorer/license/
en
Mathematical Sciences
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bc4cd1295468d5d2c0f755c8c669fcdc8df0ed89a516d111785b8ac96745e704
Pure Mathematics
Kato
Tosio
manuscripta mathematica
0025-2611
1432-1785
Springer Nature - SN SciGraph project
28
1-3
pub.1039529393
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Department of Mathematics, University of California, 94720, Berkeley, CA, USA
University of California, Berkeley
10.1007/bf01647967
doi