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Conservation laws play an important role in science. The aim of this thesis is to provide an overview and develop new methods for constructing conservation laws using Lie group theory. The derivation of conservation laws for invariant variational problems is based on Noether’s theorem. It is shown that the use of Lie-Bäcklund transformation groups allows one to reduce the number of basic conserved quantities for differential equations obtained by Noether’s theorem and construct a basis of conservation laws. Several examples on constructing a basis for some well-known equations are provided. Moreover, this approach allows one to obtain new conservation laws even for equations without Lagrangians. A formal Lagrangian can be introduced and used for computing nonlocal conservation laws. For self-adjoint or quasi-self-adjoint equations nonlocal conservation laws can be transformed into local conservation laws. One of the fields of applications of this approach is electromagnetic theory, namely, nonlocal conservation laws are obtained for the generalized Maxwell-Dirac equations. The theory is also applied to the nonlinear magma equation and its nonlocal conservation laws are computed.

Conservation laws play an important role in science. The aim of this thesis is to provide an overview and develop new methods for constructing conservation laws using Lie group theory. The derivation of conservation laws for invariant variational problems is based on Noether’s theorem. It is shown that the use of Lie-Bäcklund transformation groups allows one to reduce the number of basic conserved quantities for differential equations obtained by Noether’s theorem and construct a basis of conservation laws. Several examples on constructing a basis for some well-known equations are provided. Moreover, this approach allows one to obtain new conservation laws even for equations without Lagrangians. A formal Lagrangian can be introduced and used for computing nonlocal conservation laws. For self-adjoint or quasi-self-adjoint equations nonlocal conservation laws can be transformed into local conservation laws. One of the fields of applications of this approach is electromagnetic theory, namely, nonlocal conservation laws are obtained for the generalized Maxwell-Dirac equations. The theory is also applied to the nonlinear magma equation and its nonlocal conservation laws are computed. / <p>Thesis for the degree of Doctor of Philosophy</p>

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

The global crisis of biodiversity depletion sets the stage for a necessary re-definition of State self-interest in the international milieu. That re-definition is effected by a changing perception of 'self'; one that occurs through the mental lens of interdependence and long-term vision. This thesis attempts to challenge conventional precepts and present a submission for change by drawing upon constructivist thought, which asserts that current perceptions are socially constructed and rooted in "collective intentionality", such that what has been human-made can be altered by the same processes through which it came into existence. In so doing, the author employs the notions of international ethics as a shared belief and international law as an ideational instrument to facilitate that change in favor of international cooperation toward the necessary amelioration of global biodiversity diminution in order to assure our future.

In this investigation, a review is undertaken of the newly promulgated and existent legislation pertaining to the conservation of biodiversity, and the establishment of protected areas as the primary means to protect representative samples thereof. This review develops understanding of the various types of protected areas which may be used, in a broad sense, to conserve the country's biodiversity, with special reference being made to the recently promulgated Protected Areas Act. In undertaking this, a detailed discussion of biodiversity, trusteeship and the concept of systematic planning and irreplaceability is generated. Cursory comment and discussion in a socio-political context, in particular regarding land reform, as well as the various international obligations and commitments the country has undertaken, is made. Despite South Africa being the third most biologically diverse country globally, it is concluded that the conservation of its biodiversity has had a troubled and undirected history. The establishment of protected areas, as a result, has been ad hoc and potentially ineffective at a national scale. The source of this observation is linked directly to the absence of a structured and co-ordinated framework that supports the fulfilment of the country's international commitments to conserve biodiversity. The promulgation of the Biodiversity Act and subsequently the Protected Areas Act, has brought into playa significant step forward in developing this co-ordinated framework. The Act clarifies and brings effect to the State's trusteeship as well as providing a platform for the participation of a wider range of role players, especially previously disadvantaged and land dispossessed communities, in conservation and protection of biodiversity. This participation includes conserving biodiversity for economic, social, and cultural reasons. The absence of meaningful incentives for private and communal landowners to voluntarily conserve biodiversity, and the significance ofthis, is also discussed. Finally a consideration is given of the secondary aim of this legislation, to simplify the statutes concerning the conservation of biodiversity and particularly those pertaining to protected area establishment. This simplification is only partially achieved as a number of protected areas are still not at all or partially regulated by the Protected Areas Act. This may be a source of confusion and uncertainty. / Thesis (LL.M.)-University of KwaZulu-Natal, Pietermaritzburg, 2005.

Conservation agreements have been used successfully around the globe for the conservation of biodiversity on private land. In South Africa however, their use to this end has largely been overlooked. Conservation mechanisms in the country have focussed primarily on traditional methods; establishing and managing protected areas identified as having some form of conservation significance. At present only 5.8% of land in South Africa is conserved in statutory protected areas, however government has committed itself to increasing this percentage to 8%. Furthermore, many of the country's biodiversity-rich areas are situated on private land and are currently afforded little or no protection. The cost of purchasing the land is not only financially prohibitive but also socially unacceptable and consequently alternative conservations mechanisms need to be explored. This study provides a comparative analysis of the legislation governing conservation agreements in the United States, Canada, Australia and New Zealand and highlights several common key provisions which have contributed to the success of these agreements. It also provides recommendations on possible changes to the South African legislation to allow for a more effective contribution by private landowners to biodiversity objectives and targets within the country. Although the study establishes that conservation agreements can be accommodated within South Africa's legal system it acknowledges that the success of these agreements is largely dependent on complex interactions between effective policy, supporting institutional arrangements, and attractive incentives. It cautions that if these agreements are to work in South Africa, then careful consideration needs to be given not only to tailor-making the legislation to the South African environment but also to establishing incentives which facilitate "buy-in" from landowners. / Thesis (LL.M.)-University of KwaZulu-Natal, Pietermaritzburg, 2008.

South Africa's protected areas are at the forefront of the county's efforts to conserve it's unique flora and fauna. The setting aside of these vast tracts of land has been the main thrust of Western conservation efforts for over two centuries. Despite the significant financial and human resources allocated to the protection of these natural areas, the extinction of many plant and animal species continues to occur on a daily basis. This study sets out to explore one of the crucial weaknesses of traditional protected areas management - the failure to incorporate and empower the people with the greatest knowledge and need of the natural resources in their areas - the local indigenous communities. In the past, the legislative focus was aimed at the total exclusion of these communities from protected areas. In South Africa, these 'preservationist' laws have been bitterly flavoured by the apartheid ideology, resulting in widespread environmental inequity and injustice for those societies targeted by racist and discriminatory policies. The thesis traces the history of the national parks concept, from its preservationist origin in the late nineteenth century United States, to modern day national parks that operate in terms of joint-management agreements in Australia and South Africa. It also exposes the detrimental effect that the establishment of national parks has inflicted on local indigenous communities around the globe. The experiences of Zimbabwe, Namibia, Canada and Australia are of particular relevance and value to South Africa in this respect. An overview and assessment of the current legal regime governing protected areas in South Africa reveals that further legislative transformation is required in order to integrate human development and wildlife conservation ideals. In particular, greater emphasis is needed to ensure the participation of local indigenous communities in the management natural resources in and around national parks. A failure to meet this objective may seriously undermine the future well-being of all of South Africa's inhabitants. / Thesis (LL.M.)-University of Natal, Pietermaritzburg, 2002.

Prior to the commencement of the Convention on Biological Diversity (CBD), genetic resources were considered to be the common heritage of mankind; this principle gave the right to developed countries to obtain and freely use the genetic material of developing countries. Growing concern over the controversial ‘free access’ system and the monopolization of benefits led to the negotiation of an international treaty, the CBD, to regulate access to genetic resources and the sharing of benefits resulting from the utilisation of such resources. The CBD makes some important innovations. It recognizes that the authority to determine access to genetic resources depends on national governments and is subject to national legislation. Thus, the CBD recognizes state sovereignty over genetic resources and institutes the principles of Prior informed Consent (PIC), Mutually Agreed Terms and Benefit-Sharing. However, the CBD and other international instruments relating to genetic resources have not had the desired effect of preventing the misappropriation of genetic resources and associated traditional knowledge (TK). Developing countries suffered and continue to suffer from the piracy of their resources. This state of affairs has led to the recent adoption of the ‘Nagoya Protocol on Access to Genetic Resources and the Fair and Equitable Sharing of Benefits Arising from their Utilization to The Convention on Biological Diversity,’ (2010 Nagoya Protocol). This dissertation will consider the contribution of the Nagoya Protocol to the existing global and regional instruments concerning the access and benefit sharing of genetic resources. After explaining the gaps in the existing instruments, it will explore whether the Protocol is a miracle solution to the recurrent concern over misappropriation of genetic resources from biologically rich countries, or whether there is still much work to do to sort out this problem. / Thesis (LL.M.)-University of KwaZulu-Natal, Pietermaritzburg, 2012.

Mooney-Rivlin hyperelasticity equations are nonlinear coupled partial differential equations (PDEs) that are used to model various elastic materials. These models have been extended to account for fiber reinforced solids with applications in modeling biological materials. As such, it is important to obtain solutions to these physical systems. One approach is to study the admitted Lie symmetries of the PDE system, which allows one to seek invariant solutions by the invariant form method. Furthermore, knowledge of conservation laws for a PDE provides insight into conserved physical quantities, and can be used in the development of stable numerical methods. The current Thesis is dedicated to presenting the methodology of Lie symmetry and conservation law analysis, as well as applying it to fiber reinforced Mooney-Rivlin models. In particular, an outline of Lie symmetry and conservation law analysis is provided, and the partial differential equations describing the dynamics of a hyperelastic solid are presented. A detailed example of Lie symmetry and conservation law analysis is done for the PDE system describing plane strain in a Mooney-Rivlin solid. Lastly, Lie symmetries and conservation laws are studied in one and two dimensional models of fiber reinforced Mooney-Rivlin materials.