Mixed problems for the Korteweg-de Vries equation

Results are established concerning the non-local solubility and well posedness in various function spaces of the mixed problem for the Korteweg-de Vries equation u(t) + u(xxx) + au(x) + uu(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 --> +infinity or x --> -infinity. Application of this boundary potential enables us in particular to prove the existence of generalized solutions with non-regular boundary values.

Authors
Editors
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Publisher
Russian Academy of Sciences
Number of issue
5-6
Language
English
Pages
903-935
Status
Published
Department
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Link
-
Number
-
Volume
190
Year
1999
Organizations
-
Keywords
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Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/9211/