Originally presented as author's thesis, Bonn, 1983. / Bibliography: p. [221]-[225]

Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 1991. / Includes bibliographical references (p. 199-201).

Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2005. / Includes bibliographical references: p. 116-119.

In this dissertation we analyse from a qualitative standpoint motion in a quasihomogeneous potential field: we offer a complete description of the flow associated with the two-body problem in quasihomogeneous field, obtain necessary and sufficient conditions for the block regularization of the flow and we propose an alternative model for the helium atom within the framework of a Manev-type interaction. We call a potential quasihomogeneous if it is of the form A/rᵃ + B/rᵝ, where r is the distance between the two mass points, 0 < α < β are real parameters and A > 0 and B > 0 inertia factors. To obtain the full description of the flow associated with the two-body problem in quasihomogeneous fields, we use diffeomorphic transformations that lead to an equivalent analytic system and at least differentiable integral energy relation. For each level of energy, we introduce the fictional invariant collision manifold and the infinity manifolds. We offer and analyse the global flow picture and we point out the Lebesgue measure of the set of initial conditions that lead to collision for each different case with respect to α and β. The next chapter focuses on the smoothness of the flow in the neighborhood of the collision manifold. In question is the possibility of extending solutions beyond singularities maintaining good properties with respect to initial data. In this case the singularity set for the system is said to be block regularizable. It is proved that the singularity set block regularizable if and only if β = 2 − [special characters omitted], where n is a positive integer, n ≥ 2. Also, the physical interpretation of this result is pointed out, namely that block regularization is in fact the mathematical expression of constrain imposed over the classical scattering angle. The last chapter presents a model for the Helium atom within the framework of classical mechanics. The set up consists of a planar isosceles 3-body problem formed by one neutron and two electrons, whose law of motion is given by a Manev-type potential with charges. We first describe the qualitative features of the local flow near triple collision, find several properties of the global flow and finally we prove the existence of a large open, connected, positive-measure manifold of bounded and collisionless solution. / Graduate

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.

In this work, we study how solutions of certain non-compact geometric flows of fast-diffusion type interact with their asymptotic geometries at infinity. In the first part, we show the long time existence theorem to the inverse mean curvature flow for complete convex non-compact initial hypersurfaces. The existence and behavior of a solution is tied with the evolution of its tangent cone at infinity. In particular, the maximal time of existence can be written in terms of the area ratio between the initial tangent cone at infinity and the flat hyperplane. In the second part, we study the formation of type II singularity for non-compact Yamabe flow. Assuming the initial metric is conformally flat and asymptotic to a cylinder, we show the higher order asymptotics of the metric determines the curvature blow-up rates at the tip in its first singular time. We also show the singularities of such solutions are modeled on rotationally symmetric steady gradient solitons.

Thesis (M.S.)--Brigham Young University. Dept. of Mathematics, 2008. / Includes bibliographical references (p. 45-46).

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Thesis (Ph. D.)--University of Washington. / Bibliography: l. 73-74.