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A model of a three species intraguild predation community is proposed. The model is realized as a system of cross-diffusion equations which allow the intraguild prey species to adjust its motility based on local resource and intraguild predator densities. Solutions to the cross-diffusion system are shown to exist globally in time and the existence of a global attractor is proved. Abstract permanence theory is used to study conditions for coexistence in the ecological community. The case where the intraguild prey disperses randomly is compared to the case where the intraguild prey disperses conditionally on local ecological fitness and it is shown that the ability of the intraguild prey to persist in the ecological community is enhanced if the intraguild prey utilizes a movement strategy of avoiding areas with negative fitness. A finite element scheme is used to numerically simulate solutions to the system and confirm the analytical results.

Made available in DSpace on 2014-06-11T19:24:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-05-07Bitstream added on 2014-06-13T20:07:58Z : No. of bitstreams: 1 martins_j_me_rcla.pdf: 650990 bytes, checksum: 197553843285b3dcdd899cddf89d0ab2 (MD5) / Universidade Estadual Paulista (UNESP) / Neste trabalho caracterizamos o conjunto dos pontos de equilíbrio de um problema parabólico quasilinear governado pelo p-Laplaciano, p > 2, e do problema parabólico governado pelo Laplaciano / In this work we give a characterization set of the equilibrium points of a parabolic problem quasi-linear governed by the p-Laplacian, p > 2, and the a parabolic problem governed by the Laplacian

The production of long, thin polymeric fibers is a main objective of the textile industry. Melt-spinning is a particularly simple and effective technique. In this work, we shall discuss the equations of melt-spinning in viscous and viscoelastic flow. These quasilinear hyperbolic equations model the uniaxial extension of a fluid thread before its solidification. We will address the following topics: first we shall prove existence, uniqueness, and regularity of solutions. Our solution strategy will be developed in detail for the viscous case. For non-Newtonian and isothermal flows, we shall outline the general ideas. Our solution technique consists of energy estimates and fixed-point arguments in appropriate Banach spaces. The existence result for a simple transport equation is the key to understanding the quasilinear case. The second issue of this exposition will be the stability of the unforced frost line formation. We will give a rigorous justification that, in the viscous regime, the linearized equations obey the ``Principle of Linear Stability''. As a consequence, we are allowed to relate the stability of the associated strongly continuous semigroup to the numerical resolution of the spectrum of its generator. By using a spectral collocation method, we shall derive numerical results on the eigenvalue distribution, thereby confirming prior results on the stability of the steady-state solution. / Ph. D.

Orientador: Marcos Tadeu de Oliveira Pimenta / Resumo: Para uma classe de equações quasilineares de Schrödinger, estabelecemos a existência de soluções positivas e nodais pelo método de Nehari. / Abstract: For a class of Schrödinger quasilinear equations, we established the existence of positive and nodal solutions by the Nehari method. / Mestre

Cette thèse traite des Équations aux Dérivées Partielles Stochastiques Quasilinéaires. Elle est divisée en deux parties. La première partie concerne le problème d’obstacle pour les équations aux dérivées partielles stochastiques quasilinéaires et la deuxième partie est consacrée à l’étude des équations aux dérivées partielles stochastiques quasilinéaires dirigées par un G-mouvement brownien. Dans la première partie, on montre d’abord l’existence et l’unicité d’un problème d’obstacle pour les équations aux dérivées partielles stochastiques quasilinéaires (en bref OSPDE). Notre méthode est basée sur des techniques analytiques venant de la théorie du potentiel parabolique. La solution est exprimée comme une paire (u,v) où u est un processus prévisible continu qui prend ses valeurs dans un espace de Sobolev et v est une mesure régulière aléatoire satisfaisant la condition de Skohorod. Ensuite, on établit un principe du maximum pour la solution locale des équations aux dérivées partielles stochastiques quasilinéaires avec obstacle. La preuve est basée sur une version de la formule d’Itô et les estimations pour la partie positive d’une solution locale qui est négative sur le bord du domaine considéré. L’objectif de la deuxième partie est d’étudier l’existence et l’unicité de la solution des équations aux dérivées partielles stochastiques dirigées par G-mouvement brownien dans le cadre d’un espace muni d’une espérance sous-linéaire. On établit une formule d’Itô pour la solution et un théorème de comparaison. / This thesis deals with quasilinear Stochastic Partial Differential Equations (in short SPDE). It is divided into two parts, the first part concerns the obstacle problem for quasilinear SPDE and the second part solves quasilinear SPDE driven by G-Brownian motion. In the first part we begin with the existence and uniqueness result for the obstacle problem of quasilinear stochastic partial differential equations (in short OSPDE). Our method is based on analytical technics coming from the parabolic potential theory. The solution is expressed as a pair (u, v) where u is a predictable continuous process which takes values in a proper Sobolev space and v is a random regular measure satisfying minimal Skohorod condition. Then we prove a maximum principle for a local solution of quasilinear stochastic partial differential equations with obstacle. The proofs are based on a version of Itô’s formula and estimates for the positive part of a local solution which is negative on the lateral boundary. The objective of the second part is to study the well-posedness of stochastic partial differential equations driven by G-Brownian motion in the framework of sublinear expectation spaces. One can also establish an Itô formula for the solution and a comparison theorem.

In this paper, by a new constructive method, the authors reprove the global exact boundary controllability of a class of quasilinear hyperbolic systems of conservation laws with linearly degenerate fields. It is shown that the system with nonlinear boundary conditions is globally exactly boundary controllable in the class of piecewise C¹ functions. In particular, the authors give the optimal control time of the system. Finally, a new application is also given.

Orientador: Marcelo da Silva Montenegro / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Cientifica / Made available in DSpace on 2018-08-16T14:07:09Z (GMT). No. of bitstreams: 1 Melo_AlisonMarceloVanDerLaan_M.pdf: 595460 bytes, checksum: f3496cc25c882ea841e02b15bffe5256 (MD5) Previous issue date: 2010 / Resumo: Observação: O resumo, na íntegra poderá ser visualizado no texto completo da tese digital / Abstract: Note: The complete abstract is available with the full electronic digital thesis or dissertations / Mestrado / Matematica / Mestre em Matemática

In this work we apply the method of hydrodynamic reductions to study the integrability of the class of second order quasilinear equations.