On the Korteweg-de Vries equation
Copyright policy )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.
- DigiZeitschriften Germany
- University of California, Berkeley United States
Partial differential equations of mathematical physics and other areas of application, existence, Initial value problems for linear higher-order PDEs, uniqueness, Sobolev space, Article, Higher-order parabolic equations, 510.mathematics, continuous dependence, Korteweg-de Vries equation, General existence and uniqueness theorems (PDE), Initial-boundary value problems for higher-order parabolic equations, quasi-linear evolution equations
Partial differential equations of mathematical physics and other areas of application, existence, Initial value problems for linear higher-order PDEs, uniqueness, Sobolev space, Article, Higher-order parabolic equations, 510.mathematics, continuous dependence, Korteweg-de Vries equation, General existence and uniqueness theorems (PDE), Initial-boundary value problems for higher-order parabolic equations, quasi-linear evolution equations
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