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.
Results
Showing 1 to 20 of 25 for “"weak solutions"”.
-
L² decay for weak solutions of the micropolar equations on R³
We obtain decay estimates for solutions of the micropolar fluid equations . Such equations, proposed by A. C. Eringen, generalize the classic model of Navier-Stokes and describe the behavior of fluids with microstructure such as animal blood, liquid crystals, suspensions, among others. For this, we …
-
On the convergence of higher-order finite element methods to weak solutions
… partial differential equations (PDEs). Discrete solutions to the PDE must converge to weak solutions in order for the discontinuity propagation speed to be correct. As shown by the Lax-Wendroff theorem, one method to guarantee that convergence, if it occurs, will be to a weak solution is to use a …
-
Constructive Analysis of Partial Differential Equations
… presents the results produced in the study of weak solutions of the Dirichlet Problem within Errett Bishop's constructive mathematics. It roughly falls into three major parts: a critical analysis of the classical approaches from a constructive point of view (Chapter 2); constructive results on …
-
Global a priori Estimates and Sharp Existence Results for Quasilinear Equations on Nonsmooth Domains.
… global unweighted a priori estimates for very weak solutions below the natural exponent and weighted estimates at the natural exponent. The weights we consider are the well studied Muckenhoupt weights. Using the results obtained in Chapter 4, we obtain sharp existence result for quasilinear …
-
Solution of conservation laws via convergence space completion
… problem. For this reason, suitable generalized solutions of such problems, known as weak solutions, have been considered and studied extensively. However, weak solutions are not unique. In order to obtain a unique solution that is physically relevant, the vanishing viscosity method, amongst …
-
Sobre a teoria de regularidade elíptica via análise da equação de Helmholtz em RN
… that this result can also be used to regularize weak solutions of nonlinear elliptic problems in RN. In order to achieve our goals, it will be of vital importance the use of Bessel’s Modified Function Theory, Calderón-Zygmund Theory, the Mountain Pass Theorem and Schauder’s Theorem, as well as …
-
Modeling Collective Behavior of Dislocations in Crystalline Materials
… loop and operation of a Frank-Read source. The weak solutions to these equations are not unique, and the numerical method is able to capture solutions corresponding to shock as well as expansion fans.
-
One-Dimensional Fractal Wave Equations
… cannot be appled. First, by using a weak formulation of the problem, we prove the existence, uniqueness and regularity of weak solutions of these wave equations. Second, we study numerical computations of the solutions. By using the second-order self-similar identities introduced by …
-
Boundary value and Wiener-Hopf problems for abstract kinetic equations with nonregular collision operators
… Hilbert space. For unbounded A’s we consider weak solutions in a larger space H<sub>T</sub>, which has a natural Krein space structure. Using the Krein space geometry considerably simplifies the analysis of the question of unique solvability.
-
Regularity theory for nonlocal equations
… for an arbitrarily small gain of integrability, weak solutions $u \in W^{s,2}$ in fact belong to $W^{t,p}_{loc}$ for any $s \leq t < \min\{2s,1\}$, where $p>2$ reflects the amount of integrability gained. By embedding, we also obtain optimal higher Hölder regularity for such nonlocal …
-
Nonlinear Pseudoparabolic Equations and Variational Inequalities
… thesis is to prove existence and uniqueness of weak solutions for 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 …
-
ANALYSIS OF TWO CLASSES OF CROSS DIFFUSION SYSTEMS
… point theorem, existence of the fully discrete solutions is shown. By using entropy-type inequalities and compactness arguments, the convergence of the approximation of each system is proved and hence existence of a global weak solution is obtained. Providing further regularity of the solution …
-
Self-shrinkers of mean curvature flow and harmonic map heat flow with rough boundary data
… we prove the uniqueness for energy decreasing weak solutions of the harmonic map heat flow from the unit open disk into a closed manifold, given any H¹ initial data and boundary data, which is the restriction of the initial data on the boundary of the disk. Previously, under an additional …
-
Computing upper and lower bounds on linear functional outputs from linear coercive partial differential equations
… values of linear functional outputs of the exact weak solutions to linear coercive partial differential equations with piecewise polynomial forcing posed on polygonal domains. The method results from exploiting the Lagrangian saddle point property engendered by recasting the output problem as a …
-
On Generalized Solutions to Some Problems in Electromagnetism and Geometric Optics
… methods from functional analysis, global in time solutions to initial boundary value problems with general nonzero boundary data and nonzero current density are obtained, only assuming the material parameters are bounded and measurable. This problem is motivated by an electromagnetic inverse …
-
Existence Results for Plasma Physics Models Containing a Fully Coupled Magnetic Field
… is on existence and uniqueness questions for solutions of the initial value problem, i.e., it is asked whether there exists a solution f of the system under consideration such that f(t=0)=f0 where f0 is a prescribed initial datum. In order to answer this question further properties of …
-
Some Stationary and Evolution Problems Governed by Various Notions of Monotone Operators
… the end to examine new problems and provide some solutions. Variational approach will be used to reformulate these problems into stationary equations (in the case of BVPs) and evolution equations (in the case of IBVPs), where the underlined operators constructed as realizations of those problems …
-
Anisotropic nonlinear PDE models and dynamical systems in biology
… and neural networks. We study the existence of solutions to this model and propose an adaptation so that a macroscopic system can be obtained as its formal continuum limit. For the spatially two-dimensional rectangular setting we prove the rigorous continuum limit of the constrained energy …
-
Dewetting of thin solid films
… sharp interface limits, existence of solutions, numerical simulations and linear stability analysis of the dewetting front. We start with the formulation of a two-dimensional anisotropic phase field model for solid state dewetting on a solid substrate. The evolution is described by a …
-
Gas-Phase Epoxidation of Ethylene and Propylene
… supports (Au/TS-1). Catalysts treated with weak solutions of sodium cyanide resulted in preferential removal of small gold particles, while catalysts treated with strong solutions resulted in dissolution of the gold and re-precipitation as gold (+1) cyanide. X-ray absorption spectroscopy …
Page 1 of 2