Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 182-190). Also available via the Internet.

Typescript (photocopy). / Digitized by Kansas Correctional Industries

In this thesis, we study nonlinear partial differential equations arising from image processing and cheomotaxis. We analyze mathematical models in conservative form from the perspective of traveling wave solutions. We show the existence and the stability of traveling wave solutions in the models, which helps to understand the behaviors of solutions in the models. The thesis largely consists of two parts: (1) We develop stability analysis for a traveling wave solution of a nonlinear conservation law arising from image processing. To be specific, we prove that if the initial perturbation between a solution and a traveling wave solution to the problem is small, the solution converges to the traveling wave solution.To show this, we construct a weight function in establishing energy estimates to overcome difficulties caused by the absence of the convexity of a flux of the conservation law. (2) We develop dynamical systems theory to study traveling wave solutions in a chemotaxis model. A traveling wave solution to the model in a partial differential equation is a heteroclinic/homoclinic orbit to the model in an ordinary differential equation. Thus, we investigate the existence and non-existence of a heteroclinic/homoclinic orbit in certain ranges of parameters in the model by applying dynamical systems theory.

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Abstract not available. / Thesis (M.LL.)-University of Natal, Pietermaritzburg, 1995.

published_or_final_version / Environmental Management / Master / Master of Science in Environmental Management

A system of nonlinear di fferential equations, namely, the Belousov-Zhabotinskii reaction model has been investigated for nonlinear self-adjointness using the recent work of Professor N.H.Ibragimov. It is shown that the model is not nonlinearly self-adjoint. The symmetries of the system and nonlinear conservation laws are calculated. The modi fied system, which is nonlinearly self-adjoint, is also analysed. Its symmetries and conservation laws are presented.

This thesis examines the influence of contemporary approaches to biodiversity conservation on conceptions of state sovereignty over natural resources. Traditional approaches to state sovereignty have emphasized the right of states to exploit natural resources. Contemporary approaches to biodiversity conservation, however, have given rise to a more flexible and dynamic understanding of state sovereignty over natural resources: one encompassing sovereign rights of exploitation along with corresponding conservation responsibilities. Founded upon this premise, the thesis focuses on the emergence of a 'balanced' approach to state sovereignty over natural resources and examines its effects on the role of states in managing natural resources. While addressing it as the basis of the emergence of the recognition of a duty of environmental protection, inter alia, in the form of biodiversity conservation and sustainable use of biological resources, the author suggests that the balanced approach to state sovereignty has been instrumental in redefining the role of states, and the role of the sovereignty principle itself in achieving the goal of biodiversity conservation.

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