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 25 for “"Parabolic equations"”.
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Parabolic equations without a minimum principle
In this thesis, we consider several parabolic equations for which the minimum principle fails. We first consider a two-point boundary value problem for a one dimensional diffusion equation. We show the uniqueness and existence of the solution for initial data, which may not be continuous at two …
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Similarity solutions of stochastic nonlinear parabolic equations
… solutions of the nonlinear stochastic complex parabolic equation in the presence of two profiles. Specifically, the randomly modulated linear potential and the randomly perturbed quadratic focusing medium. In the former, a class of solutions is shown to admit an exact statistical description in …
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Equivariant Global Hopf Bifurcation in Abstract Nonlinear Parabolic Equations
… global symmetric Hopf bifurcation in abstract parabolic systems by means of the twisted equivariant degree.
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Controllability of quasilinear parabolic equations and Ladyzhenskaya-Boussinesq models
Neste presente trabalho, estudamos diferentes tipos de controle em dois modelos interes- santes, tanto teóricos quanto aplicados. No capítulo 2, estudaremos a existência de equilíbrios de Nash para a equação do calor com coeficiente de viscosidade dependendo do estado; também realizamos a parte …
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Pointwise Schauder Estimates of Parabolic Equations in Carnot Groups
… for certain classes of partial differential equations. Since that time, they have remained an essential tool in the field. Roughly speaking, the estimates state that the Holder continuity of the coefficient functions and inhomogeneous term implies the Holder continuity of the solution and its …
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A Polynomial Based Iterative Method for Linear Parabolic Equations
… developed to integrate multi-dimensional linear parabolic initial-boundary-value problems. It is based on $L\sb2$-approximations to $f(z) = (1 - exp(-z))/z,f(0) = 1,$ over ellipses in the complex plane using expansions of f in Chebychev polynomials. The calculation of the Fourier Coefficients …
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Some results on degenerate parabolic equations not in divergence form
… problems for second-order quasilinear degenerate parabolic equations not in divergence form. After establishing existence and uniqueness results in the first chapter, in Chapters 2 through 6 more special problems of the above type are investigated and in particular the large time behavior of …
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On upper bounds for waiting times for doubly nonlinear parabolic equations
… nonnegative solutions for degenerated diffusion equations depends on the growth of the initial value. The situation of the porous medium equation is fully understood thanks to the works of Aronson, Alikakos, Caffarelli, Chipot, Kamin, Sideris (1983-1985). Although lower bounds, e. g. by …
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Analysis and numerical approximations of exact controllability problems for systems governed by parabolic differential equations
… problems for systems modeled by linear parabolic differential equations and the Burger's equations are considered. A condition on the exact controllability of linear parabolic equations is obtained using the optimal control approach. We also prove that the exact control is the limit of …
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Reaction-Diffusion Systems with Discontinuous Reaction Functions
… of solutions for a coupled system of two parabolic equations and the second part is devoted to the monotone iterative methods for monotone and mixed quasimonotone functions. Various monotone iterative schemes are presented and each of these schemes leads to an existence-comparison theorem …
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Eternal Solutions and Heteroclinic Orbits of a Semilinear Parabolic Equation
… of heteroclinic orbits for a class of semilinear parabolic equations, focusing primarily on the case where the nonlinearity is a second degree polynomial with variable coefficients. Along the way, a new and elementary proof of existence and uniqueness of solutions is given. Heteroclinic orbits are …
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The evolution equation for closed magnetic geodesics
… to a system of (nonlinear) ordinary differential equations of second order. But we are only interested in periodic solutions. To this end, we study the corresponding system of (nonlinear) parabolic equations for closed magnetic geodesics and, as a main result, eventually prove the existence of …
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Numerical detection of complex singularities in two and three dimensions
… often occur in solutions to partial differential equations; important examples include the formation of shock fronts in hyperbolic equations and self-focusing type blow up in nonlinear parabolic equations. Information about formation and structure of singularities can have significant role in …
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Energy methods for nonsymmetric nonlocal operators
… is to develop the regularity theory for nonlocal parabolic equations. We focus on problems driven by nonlocal operators associated with nonsymmetric bilinear forms. In contrast to the symmetric case, nonsymmetric nonlocal operators have not yet been studied systematically. Our main results contain …
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Nonlinear Pseudoparabolic Equations and Variational Inequalities
… some types of quasilinear and nonlinear pseudoparabolic equations and for some types of quasilinear and nonlinear variational inequalities. The pseudoparabolic equations are characterized by the presence of mixed third order derivatives. Here the existence theory for degenerate parabolic …
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Nonstandard Models in Measure Theory and in functional Analysis
… for a class of ill-posed forward-backward parabolic equations, and on the study of the regularity and asymptotic behaviour of its nonstandard solutions. This approach proved to be a viable alternative to the study of the vanishing viscosity limit of the solution of a pseudoparabolic …
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A three-dimensional coupled modes solution for range-dependent waveguides
… great achievements obtained with fast-field and parabolic equation models, normal mode programs still remain a very efficient, simple and practical tool for describing ocean acoustics in range-independent environments. Numerical implementations of wave-theory solutions for range-dependent …
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A theoretical investigation of thermal waves
… The resulting temperature and flux field equations become hyperbolic rather than the usual classical parabolic equations encountered in heat conduction. In this formulation, heat propagates at a finite speed and removes one of the anomalies associated to parabolic heat conduction, i.e., …
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Stochastic dynamics with singular lower order terms in finite and infinite dimensions
… the first part, we study a class of second order parabolic equations $$nabla (a(t,x) cdot nabla u(t,x))+b(t,x)cdot nabla u(t,x)+V(t,x) u(t,x)-partial_{t}u(t,x)=0 eqno (1)$$ in the domain $[0,T]times mathbb{R}^{d}$, where $T<infty$. We assume that the matrix $a(t,x)=(a_{ij} t,x))$ is symmetric and …
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