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On analysis of some nonlinear systems of partial differential equations of continuum mechanicsSteinhauer, Mark. January 2003 (has links)
Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2002. / Includes bibliographical references (p. 113-119).
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Continuous symmetries, lie algebras and differential equationsEuler, Norbert 11 February 2014 (has links)
D.Sc. (Mathematics) / In this thesis aspects of continuous symmetries of differential equations are studied. In particular the following aspects are studied in detail: Lie algebras, the Lie derivative, the jet bundle formalism for differential equations, Lie point and Lie-Backlund symmetry vector fields, recursion operators, conservation laws, Lax pairs, the Painlcve test, Lie algebra valued differenmtial forms and Dose operators as a representation of differential operators. The purpose of the study is to gain a better understanding of complicated nonlinear dirrerential equations that describe nature and to construct solutions. The differential equations under consideration were derived [rom physics and engineering. They are the following: the Kortcweg-dc Vries equation, Burgers' cquation , the sine-Gordon equation, nonlinear diffusion equations, the Klein Gordon equation, the Schrodinger equation, nonlinear Dirac equations, Yang-Mills equations, the Lorentz model, the Lotka-Volterra model, damped unharrnonic oscillators, and others. The newly found results and insights are discussed in chapters 8 to 17. Details on the COli tents of each chapter and rcfernces to some of my articles arc given in chapter 1.
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Nonlinear field equations and Painleve testEuler, Norbert 29 May 2014 (has links)
M.Sc. (Theoretical Physics) / Please refer to full text to view abstract
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Applications of lie symmetry techniques to models describing heat conduction in extended surfacesMhlongo, Mfanafikile Don 09 January 2014 (has links)
A research thesis submitted to the Faculty of Science, University of
the Witwatersrand, Johannesburg, in fulfillment of the
requirement for the degree of Doctor of Philosophy.
August 7, 2013. / In this thesis we consider the construction of exact solutions for models describing
heat transfer through extended surfaces (fins). The interest in the solutions
of the heat transfer in extended surfaces is never ending. Perhaps this is because
of the vast application of these surfaces in engineering and industrial
processes. Throughout this thesis, we assume that both thermal conductivity
and heat transfer are temperature dependent. As such the resulting energy
balance equations are nonlinear. We attempt to construct exact solutions for
these nonlinear models using the theory of Lie symmetry analysis of differential
equations.
Firstly, we perform preliminary group classification of the steady state
problem to determine forms of the arbitrary functions appearing in the considered
equation for which the principal Lie algebra is extended by one element.
Some reductions are performed and invariant solutions that satisfy the Dirichlet
boundary condition at one end and the Neumann boundary condition at
the other, are constructed.
Secondly, we consider the transient state heat transfer in longitudinal rectangular
fins. Here the imposed boundary conditions are the step change in
the base temperature and the step change in base heat flow. We employ the
local and nonlocal symmetry techniques to analyze the problem at hand. In
one case the reduced equation transforms to the tractable Ermakov-Pinney
equation. Nonlocal symmetries are admitted when some arbitrary constants
appearing in the governing equations are specified. The exact steady state
solutions which satisfy the prescribed boundary conditions are constructed.
Since the obtained exact solutions for the transient state satisfy only the zero
initial temperature and adiabatic boundary condition at the fin tip, we sought
numerical solutions.
Lastly, we considered the one dimensional steady state heat transfer in fins
of different profiles. Some transformation linearizes the problem when the thermal
conductivity is a differential consequence of the heat transfer coefficient,
and exact solutions are determined. Classical Lie point symmetry methods
are employed for the problem which is not linearizable. Some reductions are
performed and invariant solutions are constructed.
The effects of the thermo-geometric fin parameter and the power law exponent
on temperature distribution are studied in all these problems. Furthermore,
the fin efficiency and heat flux are analyzed.
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Some new results on nonlinear elliptic equations and systems. / CUHK electronic theses & dissertations collectionJanuary 2011 (has links)
In Chapter 2 we study the uniqueness problem of sign-changing solutions for a nonlinear scalar equation. It is well-known that positive solution is radially symmetric and unique up to a translation. Recently, there are many works on the existence and multiplicity of sign-changing solutions. However much less is known for uniqueness, even in the radially symmetric class. In Chapter 2, we solve this problem for nearly critical nonlinearity by Lyaponov-Schmidt reduction. Moreover, we can also prove the non-degeneracy. / In Chapter 3 we are concerned with the uniqueness problem for coupled nonlinear Schrodinger equations. The problem is to classify all positive solutions. In Chapter 3, some sufficient conditions are given. In particular, we have a sufficient and necessary condition in one dimension. The proof is elementary because only the implicit function theorem, integration by parts, and the uniqueness for scalar equation are needed. / In Chapter 4 we go back to the nonlinear scalar equation and consider the traveling wave solutions. Using an infinite dimensional Lyaponov-Schmidt reduction, new examples of traveling wave solutions are constructed. Our approach explains the difference between two dimension and higher dimensions, and also explores a connection between moving fronts and the mean curvature flow. This is the first such traveling waves connecting the same states. / This thesis is devoted to the study of nonlinear elliptic equations and systems. It is divided into two parts. In the first part, we study the uniqueness problem, and in the second part, we are concerns with traveling wave solutions. / Yao, Wei. / Adviser: Jun Cheng Wei. / Source: Dissertation Abstracts International, Volume: 73-06, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 132-142). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.
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Response of nonlinear nonstationary vibrational systems with N degrees of freedom subjected to arbitrary pulse excitationsJagannathan, Mukund January 2011 (has links)
Vita. / Digitized by Kansas Correctional Industries
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Phase transitions: regularity of flat level setsSavin, Vasile Ovidiu 28 August 2008 (has links)
Not available / text
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MULTIPHASE AVERAGING OF PERIODIC SOLITON EQUATIONSForest, M. Gregory January 1979 (has links)
No description available.
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Linear, linearisable and integrable nonlinear PDEsDimakos, Michail January 2013 (has links)
No description available.
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Group analysis of the nonlinear dynamic equations of elastic stringsPeters, James Edward, II 08 1900 (has links)
No description available.
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