A survey on the Cauchy problem for the Korteweg-de Vries equation

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Durşen, Ali Kutlu (2013) A survey on the Cauchy problem for the Korteweg-de Vries equation. [Thesis]

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In this thesis, we study the Cauchy problem for the classic Korteweg-de Vries equation ut + ux + uux + uxxx = 0 for x ∈ R, t > 0 u(x, 0) = u0(x) for x ∈ R describing the propagation of long waves in shallow waters. We first use Bona and colleagues' approach of adding a regularizing term to the equation and show that the equation is well-posed for initial data u0 2 Hs, s ≥ 3, with solution lying in this space for each t globally. We then use Kato's methods of semigroup theory in nonlinear study to lower the bound on s to s > 3=2 for local solutions and to s ≥2 for global solutions.

Item Type:Thesis
Uncontrolled Keywords:Korteweg-de Vries equation. -- Cauchy problem. -- Global existence. -- Korteweg-de Vries denklemi. -- Cauchy problemi. -- Global varlık.
Subjects:T Technology > TJ Mechanical engineering and machinery > TJ163.12 Mechatronics
ID Code:26488
Deposited By:IC-Cataloging
Deposited On:14 Dec 2014 20:10
Last Modified:25 Mar 2019 17:10

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