Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 29 for “"Reaction-diffusion equations"”.
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Asymptotic Analysis of Perturbations to Travelling Wave Solutions of Nonlinear Advection-Reaction-Diffusion Equations of Fisher Type
… this thesis we examine some nonlinear advection-diffusion-reaction equations of Fisher type. First we discuss the stability properties of the equations by writing each nonlinear equation as a system of two ordinary different equations and then analyzing the stability of their equilibrium …
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Efficient computational models for pattern formation in fixed and evolving domains
… model spatial patterns formed by nonlinear reaction-diffusion equations for benchmark reaction kinetics. Computational methods for modeling reaction-diffusion equations have been presented extensively in literature. Efficiency in these computational methods, either higher convergence or …
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The application of signaling networks to cancer metastasis and cellular motility through the EGFR pathway
… model that consists of partial differential equations and signaling networks. Analysis techniques for these nonlinear reaction-diffusion equations included a study of the biological background and motivation, along with computational simulation of the various sets of models developed. The …
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Energy methods for reaction-diffusion problems
Nonlinear reaction-diffusion equations arise in many areas of applied sciences such as combustion modeling, population dynamics, chemical kinetics, etc. A fundamental problem in the studies of these equations is to understand the long time behavior of solutions of the associated Cauchy problem. …
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Stability of planar fronts for a class of reaction diffusion systems
… space-independent steady states for a class of reaction diffusion systems that arise in combustion theory and chemical-reaction models. We begin by extending the recent one-dimensional stability results for reaction diffusion equations of this type. Using spaces with exponential weights, we …
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Spatial Decay of Rotating Waves and Restrictions on Finite Disks.
In this thesis, we consider the system of reaction-diffusion equations and the behavior of the solution of such a system. The focus is to concentrate on solutions which decay at infinity. Under suitable assumptions, we prove the solution and its derivatives decay exponentially in all space. We also …
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Modelling calcite dissolution in a rotating disc reaction vessel
… problem as a set of coupled convection- reaction-diffusion equations that is not only consistent with the bulk chemistry, but is also connected with a Stefan condition for dissolution interface, treating it as a free boundary. The substantial difference in the order of magnitude of the …
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Uniform heating of thin ceramic slabs in a multimode microwave cavity
Two-dimensional reaction diffusion equations, which contain a functional and an inhomogeneous source term, are good models for describing microwave heating of thin ceramic slabs and cylinders in a multi mode, highly resonant cavity. A thin ceramic slab situated in a TEN03 rectangular cavity modeled …
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Non-Classical Symmetry Solutions to the Fitzhugh Nagumo Equation.
<p>In <em>Reaction-Diffusion</em> systems, some parameters can influence the behavior of other parameters in that system. Thus reaction diffusion equations are often used to model the behavior of biological phenomena. The Fitzhugh Nagumo partial differential equation is a reaction diffusion …
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An Optimisation-Based Approach to FKPP-Type Equations
In this thesis, we study a class of reaction-diffusion equations of the form $\frac{\partial u}{\partial t} = \mathcal{L}u + \phi u - \tfrac{1}{k} u^{k+1}$ where $\mathcal{L}$ is the stochastic generator of a Markov process, $\phi$ is a function of the space variables and $k\in …
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Stability Analysis of Unconstrained Receding Horizon Control Schemes
… time systems are induced by sampled differential equations, effects linked to employing faster sampling and, thus, more accurate discretizations are analyzed. In this context a growth condition which may, e.g., reflect continuity properties, is introduced and the proposed methodology is …
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Fine properties of stochastic evolution equations and their applications
… of SPDE, which include all stochastic evolution equations with monotone coefficients. In the second part, some properties of invariant measures and transition semigroups are investigated for SPDE with additive noise. The main tool is the dimension-free Harnack inequality, which is established by …
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Developmental models with cell surface receptor densities defining morphological position
… structure. Models are defined in the form of reaction-diffusion equations with zero flux boundary conditions coupled with ordinary differential equations. Two mechanisms of pattern formation: diffusion driven instability and hysteresis-driven mechanism are studied and their possibilities and …
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Mathematical methods for the modelling of cell migration and chemotaxis
… migration and chemotaxis with specific focus on reaction-diffusion based models on moving domains. This thesis focuses building on the previous model of cell migration and chemotaxis introduced by Neilson et al [105]. It does this by introducing new and discussing existing numerical methods in a …
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Signal transmission in epithelial layers
… This model is characterized by nonlinear reaction-diffusion type dynamics. The nonlinearities mainly arise at cell layer where feedbacks can be generated through e.g. ligand mediated ligand release. A direct consequence of this nonlinear behavior is a possibility of existence of multiple …
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MODELING THE DYNAMICS OF INFECTIOUS DISEASES WITH Latency IN SPATIALLY HETEROGENEOUS Environments
… model is given by a system of delay differential equations (DDEs). It is a generalization of the classical Kermack-McKendrick SIR model, and it preserves some properties that the Kermack-McKendrick model processes. We show that the ratio of final sizes in two patches is fully determined by the …
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Models of self-organization in biological development
… are also introduced, with specific reference to reaction-diffusion equations, and we consider some possible chemical and biochemical realizations of self-organizing kinetics. The chapter may be read in conjunction with appendix A, which gives a somewhat more in-depth study of reaction-diffusion …
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Models of self-organization in biological development
… are also introduced, with specific reference to reaction-diffusion equations, and we consider some possible chemical and biochemical realizations of self-organizing kinetics. The chapter may be read in conjunction with appendix A, which gives a somewhat more in-depth study of reaction-diffusion …
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Rate-induced tipping in a moving habitat
… concerned is described by partial differential equations (PDEs) in the form of nonlinear one-dimensional reaction-diffusion equations and reaction-convection-diffusion equations. Two distinct growth models are constructed and the moving habitat is incorporated into each model with the addition …
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Asymptotic Problems Related to Smoluchowski-Kramers Approximation
… white noise, converges to solution of the diffusion equation $\dot{q}_{t}^{\varepsilon}=b(\qe)+\sqrt{\varepsilon}\sigma(\qe) \dot{W}_{t},\ q_{0}^{\varepsilon}=q$\ as $\mu\downarrow 0$\ uniformly on any finite time interval for each fixed $\ve>0$. This is the main justification for …
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