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New results on the formation of singularities for parabolic problems. / CUHK electronic theses & dissertations collectionJanuary 2005 (has links)
First, a regularity property for global solutions of some superlinear parabolic problems is established. We obtain some new a priori estimates on the global classical solutions. Applying this property to the blow-up problem, we obtain a general criterion for the occurrence of blow-up. When applied to the study of global weak solutions, we obtain some regularity results, which answers some open questions in this topic. / In this thesis, we obtain some new results on the formation of singularities for parabolic problems. We are interested in two typical singularities in parabolic evolution problems: blow-up and quenching. / Second, dichotomy properties for some porous medium equations and some semilinear parabolic equations are discussed. Some conditions on universal quenching are also obtained. When the space dimension is one, we establish a new, strong dichotomy property. Bifurcation analysis of some stationary solutions in high dimension is also investigated. / by Zheng Gaofeng. / "June 2005." / Adviser: Chou Kai-Seng. / Source: Dissertation Abstracts International, Volume: 67-01, Section: B, page: 0310. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 84-89). / 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, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.
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EXISTENCE-THEOREMS FOR PARABOLIC DIFFERENTIAL EQUATIONS WITH FUNCTIONS WHICH DEPEND ON PAST HISTORYMilligan, Alfred William, 1939- January 1973 (has links)
No description available.
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Structural stability of periodic systemsChen, Mingxiang 12 1900 (has links)
No description available.
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Ranges of vector measures and valuationsKuhn, Zuzana 12 1900 (has links)
No description available.
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Fine and parabolic limitsMair, Bernard A. January 1982 (has links)
In this thesis, an integral representation theorem is obtained for non-negative solutions of the heat equation on X = (//R)('n-1) x (0,(INFIN)) x (0,T) and their boundary behaviour is investigated by using the abstract Fatou-Naim-Doob theorem. The boundary behaviour of positive solutions of the equation Lu = 0 on Y = (//R)('n) x (0,T), where L is a uniformly parabolic second-order differential operator in divergence form is also studied. / In particular, the notion of semi-thinness is introduced for the corresponding potential theories on X and Y and relationships between fine, semi-fine and parabolic limits are obtained. / Results of Kemper specialised to X are obtained by means of fine convergence and a Carleson-type local Fatou theorem is obtained for solutions of Lu = 0 on a union of parabolic regions.
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Theorie einer pseudoparabolischen partiellen Differentialgleichung zur Modelliurung der Lösemittelaufnahme in PolymerfeststoffenDüll, Wolf-Patrick. January 2004 (has links)
Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2004. / Includes bibliographical references (p. 74-76).
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Difference methods for ordinary differential equations with applications to parabolic equationsDoedel, Eusebius Jacobus January 1976 (has links)
The first chapter of the thesis is concerned with the construction of finite difference approximations to boundary value problems in linear nth order ordinary differential equations. This construction is based upon a local collocation procedure with polynomials, which is equivalent to a method of undetermined coefficients. It is shown that the coefficients of these finite difference approximations can be expressed as the determinants of matrices of relatively small dimension. A basic theorem states that these approximations are consistent, provided only that a certain normalization factor does not vanish. This is the case for compact difference equations and for difference equations with only one collocation point. The order of consistency may be improved by suitable choice of the collocation points. Several examples of known, as well as new difference approximations are given. Approximations to boundary conditions are also treated in detail. The stability theory of H. O. Kreiss is applied to investigate the stability of finite difference schemes based upon these approximations. A number of numerical examples are also given.
In the second chapter it is shown how the construction method of the first chapter can be extended to initial value problems for systems of linear first order ordinary differential equations. Specific examples are 'included and the well-known stability theory for these difference equations is summarized.
It is then shown how these difference methods may be applied to linear parabolic partial differential equations in one space variable after first discretizing in space by a suitable method from the first chapter. The stability of such difference schemes for parabolic equations is investigated using an eigenvalue-eigenvector analysis. In particular, the effect of various approximations to the boundary conditions is considered. The relation of this analysis to the stability theory of J. M. Varah is indicated. Numerical examples are also included. / Science, Faculty of / Mathematics, Department of / Graduate
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Fine and parabolic limitsMair, Bernard A. January 1982 (has links)
No description available.
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Numerical investigation of the parabolic mixed-derivative diffusion equation via alternating direction implicit methodsSathinarain, Melisha 07 August 2013 (has links)
A dissertation submitted to the Faculty of Science, University of the Witwatersrand, in fulfillment of the requirements for the degree of Master of Science, May 14, 2013. / In this dissertation, we investigate the parabolic mixed derivative diffusion equation modeling
the viscous and viscoelastic effects in a non-Newtonian viscoelastic fluid. The model is
analytically considered using Fourier and Laplace transformations. The main focus of the
dissertation, however, is the implementation of the Peaceman-Rachford Alternating Direction
Implicit method. The one-dimensional parabolic mixed derivative diffusion equation
is extended to a two-dimensional analog. In order to do this, the two-dimensional analog
is solved using a Crank-Nicholson method and implemented according to the Peaceman-
Rachford ADI method. The behaviour of the solution of the viscoelastic fluid model is
analysed by investigating the effects of inertia and diffusion as well as the viscous behaviour,
subject to the viscosity and viscoelasticity parameters. The two-dimensional parabolic diffusion
equation is then implemented with a high-order method to unveil more accurate
solutions. An error analysis is executed to show the accuracy differences between the numerical
solutions of the general ADI and high-order compact methods. Each of the methods
implemented in this dissertation are investigated via the von-Neumann stability analysis to
prove stability under certain conditions.
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Some results on steady states of the thin-film type equation. / CUHK electronic theses & dissertations collectionJanuary 2011 (has links)
In this thesis we study the thin-film type equations in one spatial dimension. These equations arise from the lubrication approximation to the thin films of viscous fluids which is described by the Navier-Stokes equations with free boundary. From the structural point of view, they are fourth-order degenerate nonlinear parabolic equations, with principal term from diffusion and lower order term from external forces. In Chapter one we study the dynamics of the equations when the external force is given by a power law. Classification of steady states of this equation, which is important for the dynamics, was already known. Previous numerical studies show that there is a mountain pass scenario among the steady states. We shall provide a rigorous justification to these numerical results. As a result, a rather complete picture of the dynamics of the thin film is obtained when the power law is in the range (1,3). In Chapter two we turn to the special case of the equation where the external force is the gravity. This is important, but, unfortunately not a power law. We study and classify the steady states of this equation as well as compare their energy levels. Some numerical results are also present. / Zhang, Zhenyu. / Asviser: Kai Seng Chou. / Source: Dissertation Abstracts International, Volume: 73-06, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 103-107). / 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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