THE INITIAL VALUE PROBLEM FOR THE SEQUENCE OF GENERALIZED KORTEWEG-DE VRIES EQUEATIONS

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dc.contributor.authorSALIU, A. YUSUF
dc.date.accessioned2014-02-19T12:01:44Z
dc.date.available2014-02-19T12:01:44Z
dc.date.issued1987-11
dc.descriptionA THESIS SUBMITTED TO THE POST-GRADUATE SCHOOL, AHMADU BELLO UNIVERSITY ZARIA, IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN MATHEMATICS DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE AHMADU BELLO UNIVERSITY ZARIA, (NIGERIA) NOV. 1987en_US
dc.description.abstractInterest in nonlinear dispersive wave equations focussed recently on the simplest model equation of this type, namely, u.t = uux + ux xx,' where subscripts denote partial differentiations. Kbrteweg and de-Vries first derived the equation in their study of long water waves in a (relatively shallow) channel. Recently, this equation has been derived in plasma physics and in studies of anharmonic (nonlinear) lattices. Existence and uniqueness of solutions of the above equation for appropriate initial and boundary conditions have recently been proved by Sjoberg. This dissertation focusses on the initial value problem for the sequence of generalized Korteweg de-Vries equations, namely, We have shown that for each m, solutions of the generalized Korteweg-de-Vries equations exist for all time and are uniquely determined by arbitrary initial values. The entire work has been divided into four chapters. The first chapter covers the introduction, back-ground and definitions of some basic terms. In this chapter, we have also formulated, more precisely, our main results, in a theorem. In chapter II, we stated and proved lemmas relating the various norms. Also in this chapter, an priori bound was obtained using the relationships among the norms. Chapter III concentrates on the proof of the existence of a global solution to our initial value problem. Here, we proved the first part of the theorem formulated in chapter I. The last chapter covers the proof of uniqueness of solution of the initial value problem started in chapter III. We have shown in this chapter that given an appropriate intial value the solution can be determined uniquely for all time. Notation: Theorems, lemmas, definitions and equations are numbered decimally within the section and the number of the chapter is prefixed. Equations are indicated by a parenthesis :- (1.3.2) and a definition by a bracket [1,3.2]. A theorem or lemma is indicated without parenthesis or bracket :- 1.3.2. A single number in a bracket like [3] refers to the bibliography.en_US
dc.identifier.urihttp://hdl.handle.net/123456789/2159
dc.language.isoenen_US
dc.subjectINITIAL,en_US
dc.subjectVALUE,en_US
dc.subjectPROBLEM,en_US
dc.subjectSEQUENCE,en_US
dc.subjectGENERALIZED,en_US
dc.subjectKORTEWEG-DE VRIESen_US
dc.subjectEQUEATIONS.en_US
dc.titleTHE INITIAL VALUE PROBLEM FOR THE SEQUENCE OF GENERALIZED KORTEWEG-DE VRIES EQUEATIONSen_US
dc.typeThesisen_US
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