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 23 for “"Weak solution"”.
-
On the Hausdorff dimension of a certain measure arising from a positive weak solution to a divergence type PDE
… a certain Borel measure associated to a positive weak solution of a certain quasilinear elliptic partial differential equation in a simply connected domain in the plane. We also assume that the solution vanishes on the boundary of the domain. Then it is shown that the Hausdorff dimension of this …
-
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 …
-
Mathematical and Numerical Analysis of a Pair of Coupled Cahn-Hilliard Equations with a Logarithmic Potential
… mixture. Global existence and uniqueness of a weak solution to the problem is proved using Faedo-Galerkin method. Higher regularity results of the weak solution are established under further regular requirements on the initial data. Further, continuous dependence on the initial data is …
-
Large Time Step and Overlapping Grids for Conservation Laws
… Finite Volume Method for computing numerical solutions to hyperbolic systems of conservation laws. We also consider a method of overlapping spatial grids for which variants have proved to be an important consideration in large scale applications. In practice we often run into grids which have …
-
On Initial-Boundary Value Problems for the Nonlinear Schroedinger Equation and the Ginzburg-Landau Equation
… equation (NLS) is shown in Chapter 1. The global solution to an initial-boundary value problem for the NLS is proved in Chapter 2. Global existence of the full-line problem for the Ginzburg-Landau equation (GL) is shown in Chapter 3. In Chapter 4, the following results concerning the half-line …
-
Flow and stability studies in porous media based on some non-Darcian models.
… with the theoretical study related with the solution of the Brinkman equation. An exact Cartesian-tensor form solution of the Brinkman equation is found, which facilitates the study of various boundary value problems. The problems of the flow past a porous sphere and creeping flow past a …
-
Solving transport-density equation with diffusion using the first integral method and the generalized hyperbolic functions method
… will undeniably remove the singularity and the weak solution obtained by the characteristic method. As long as, continuity equation leads to discontinuous solutions, abrupt change of the traffic density; thus the diffusion was introduced so as to prevent incrementally deformation of the wave so …
-
Existence of Solutions Via a New Variational Principle for Nonlocal Semilinear Elliptic Equations
… of this thesis is to prove the existence of a weak solution for semilinear fractional elliptic equations given by \begin{eqnarray*}\left\{ \begin{array}{ll} (-\Delta)^s u=|u|^{p-2} u+ f(x),& \quad x\in \Omega,\\ u=0, & \quad x \in \R^n \backslash \Omega, %0, & \quad x \in \partial \Oemga, …
-
Monotone and pseudomonotone operators with applications to variational problems
… Banach spaces are used to prove the existence of solutions to nonlinear elliptic boundary value problems. A well-known approach to solving nonlinear elliptic boundary value problems is to reformulate them as equations of the form A (u) = f, where A is a monotone or pseudomonotone operator from a …
-
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 …
-
Global existence in L1 for the square-well kinetic equation
… with intermolecular potential. The existence of solutions to the Cauchy problem in <i>L</i>¹. global in time and for arbitrary initial data. is proved. A simple derivation of the square-well kinetic equation is given. Lewis's method is used~ which starts from the Liouville equation of statistical …
-
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 …
-
Analysis of a Spacetime Discontinuous Galerkin Method for Systems of Conservation Laws
… Its formulation is consistent with the weak formulation of conservation laws and it naturally suggests a discrete version of the Lax entropy condition. The CSDG method is an explicit method, that is, a direct element-by-element solution procedure is possible. We investigate existence, …
-
Mixed variational problems associated with stationary viscous incompressible free boundary flows
… posed. (2) Establish regularity results for the solution of the AP. (3) Using (2) and the remaining boundary condition, determine the position of the FB. We study the existence and uniqueness of the weak solution(s) to the AP, i.e., step (1), under minimal regularity constraints on the data and …
-
Generalized Volatility-Stabilized Processes
… (2005). First, we show how to construct a weak solution of the underlying system of stochastic differential equations. In particular, we express the solution in terms of time-changed squared-Bessel processes and argue that this solution is unique in distribution. In addition, we also …
-
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 …
-
Finite element approximations for fluid flows governed by nonlinear slip boundary conditions of friction type: from theory to computations
… point strategy is used to show existence of solutions. Next we prove that the finite element approximations for the Stokes and Navier Stokes equations converge respectively to the solutions of each continuous problem. Finally, Uzawa’s algorithm is formulated and convergence of the procedure …
-
The evolution equations for Dirac-harmonic Maps
… Moreover, the existence of a short-time solution to the evolution equations is established. Chapter 4 analyzes the evolution equations in the case that the domain manifold is a closed curve. Here, the existence of a smooth long-time solution is proven. Moreover, for the regularization …
-
A study of stochastic processes in Banach spaces
… The operator Λ is closed and densely defined. A weak solution (Zt ; Bt), where Zt is centred, Gaussian and stationary while Bt is a Q-Wiener process, is given when iΛ and iΛ* generate C0 groups and the resolvent of Λ is uniformly bounded on the imaginary axis. Both Zt and Bt are stochastic …
-
Stochastic dynamics with singular lower order terms in finite and infinite dimensions
… that the parabolic equation (1) has a unique weak fundamental solution admitting two-sided Gaussian estimates. In the second part, we study the stochastic differential equation $$ dX_{t}=dW_{t}+B(t, X_{t})dt, X_{s}=x, eqno (2)$$ where $W_{t}$ is a Brownian motion and $B(t,x)$ is a …
Page 1 of 2