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A symmetry analysis of a second order nonlinear diffusion equationJoubert, Ernst Johannes 03 April 2014 (has links)
M.Sc. (Mathematics) / Please refer to full text to view abstract
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Symmetry structures and conserved forms of systems of pdesAlqurashi, Bader Mutair January 2019 (has links)
A thesis submitted in fulfillment of the requirements for the degree of Doctor of Philosophy to the Faculty of Science, University of the Witwatersrand, Johannesburg, 2019 / We will study the symmetry, invariance properties and conservation laws of partial dif
ferential equations (pdes) that arise in a number of situations in mathematical physics.
These will be range from Image Processing and noise removal algorithms to Timoshenko
beam systems. Furthermore, we will study the invariance properties and approximate
conservation laws of some nonlinear Schro¨dinger equation with PT-symmetric potentials
with inhomogeneous nonlinearity and some nonlinear Schro¨dinger equation involving a
spatially extended system consisting of two coupled elements. / TL (2019)
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Symmetry reductions, exact solutions and conservation laws of a variable coefficient (2+1)-dimensional zakharov-kuznetsov equation / Letlhogonolo Daddy Moleleki.Moleleki, Letlhogonolo Daddy January 2011 (has links)
This research studies two nonlinear problems arising in mathematical physics. Firstly
the Korteweg-de Vrics-Burgers equation is considered. Lie symmetry method is
used to obtain t he exact solutions of Korteweg-de Vries-Burgers equation. Also
conservation laws are obtained for this equation using the new conservation theorem.
Secondly, we consider the generalized (2+ 1)-dimensional Zakharov-Kuznctsov (ZK)
equation of time dependent variable coefficients from the Lie group-theoretic point
of view. We classify the Lie point symmetry generators to obtain the optimal system
of one-dimensional subalgebras of t he Lie symmetry algebras. These subalgebras arc
then used to construct a number of symmetry reductions and exact group-invariant
solutions of the ZK equation. We utilize the new conservation theorem to construct
the conservation laws of t he ZK equation. / Thesis (M. Sci in Applied Mathematics) North-West University, Mafikeng Campus, 2011
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Lie group analysis of certain nonlinear differential equations arising in fluid mechanics / Belinda Thembisa MatebeseMatebese, Belinda Thembisa January 2010 (has links)
This research studies two nonlinear differential equations arising in fluid mechanics.
Firstly, the Zakharov-Kuznetsov's equation in (3+1) dimensions with an arbitrary
power law nonlinearity is considered. The method of Lie symmetry analysis is used
to carry out the integration of Zakharov-Kuznetsov's equation. Also, the extended
tanh-function method and t he G'/G method are used to integrate the Zakharov-Kuznetsov's equation. The non-topological soliton solution is obtained by the aid of
solitary wave ansatz method. Numerical simulation is given to support the analytical
development.
Secondly. the nonlinear flow problem of an incompressible viscous fluid is considered.
The fluid is taken in a channel having two weakly permeable moving porous walls.
An incompressible fluid fills the porous space inside the channel. The fluid is magnetohydrodynamic
in the presence of a time-dependent magnetic field. Lie group
method is applied along with perturbation method in the derivation of analytic solution.
The effects of the magnetic field, porous medium, permeation Reynolds number
and wall dilation rate on the axial velocity arc shown and discussed. / Thesis (M.Sc.(Applied Mathematics) North-West University, Mafikeng Campus, 2010
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On the eigenvalues of square quaternion matrices : together with An elementary and simple proof of the connectedness of the classical groups (with Y.C. Wong); A note on some theorems for ordinary differential equations; and, On Liapounoff's stability theoremsAu-Yeung, Yik-hoi, Huang, Yung-tsou, 歐陽亦藹 January 1966 (has links)
published_or_final_version / Mathematics / Master / Master of Science
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Inertial manifoldsRobinson, James Cooper January 1995 (has links)
No description available.
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Stochastic slow-fast dynamicsLythe, Grant David January 1994 (has links)
No description available.
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Numerical treatment of oscillatory delay and mixed functional differential equations arising in modellingMalique, Md Abdul January 2012 (has links)
The pervading theme of this thesis is the development of insights that contribute to the understanding of whether certain classes of functional differential equation have solutions that are all oscillatory. The starting point for the work is the analysis of simple (linear autonomous) ordinary differential equations where existing results allow a full explanation of the phenomena. The Laplace transform features as a key tool in developing a theoretical background. The thesis goes on to explore the corresponding theory for delay equations, advanced equations and functional di erential equations of mixed type. The focus is on understanding the links between the characteristic roots of the underlying equation, and the presence or otherwise of oscillatory solutions. The linear methods are used as a class of numerical schemes which lead to discrete problems analogous to each of the classes of functional differential equation under consideration. The thesis goes on to discuss the insights that can be obtained for discrete problems in their own right, and then considers those new insights that can be obtained about the underlying continuous problem from analysis of the oscillatory behaviour of the analogous discrete problem. The main conclusions of the work are some semi-automated computational approaches (based upon the Principle of the Argument) which allow the prediction of oscillatory solutions to be made. Examples of the effectiveness of the approach are provided, and there is some discussion of its theoretical basis. The thesis concludes with some observations about further work and some of the limitations of existing analytical insights which restrict the reliability with which the approach developed can be applied to wider classes of problem.
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Stability of stochastic interval systemsSelfridge, Colin January 2000 (has links)
No description available.
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Mathematical analysis of numerical methods for dynamic structural vibration problemsOdiowei, M. O. January 1986 (has links)
No description available.
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