Sökning: "Elliptic equations"

Visar resultat 1 - 5 av 63 avhandlingar innehållade orden Elliptic equations.

1. 1. Topics in Nonlinear Elliptic Differential Equations

   Författare :Shoyeb Waliullah; Andrzej Szulkin; Thomas Bartsch; Stockholms universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Concentration-compactness principle; critical Sobolev exponent; symmetric solutions of elliptic equations; degenerate elliptic equation; Nehari manifold; Caffarelli-Kohn-Nirenberg inequality; infinitely many solutions; MATHEMATICS; MATEMATIK; Mathematics; matematik;

   Sammanfattning : In this thesis we examine the existence of solutions to nonlinear elliptic partial differential equations via variational methods.In Paper I we consider the existence of constrained minimizers which correspond to solutions of equations involving the iterated Laplacian, the iterated p-Laplacian and the critical Sobolev exponent. LÄS MER

3. 2. Two Problems in non-linear PDE’s with Phase Transitions

   Författare :Karl Jonsson; Henrik Shahgholian; Tomas Sjödin; KTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Conductivity jump; Free boundary problem; Quasilinear elliptic equation; Mathematical techniques; Nonlinear analysis; Free boundary; Free-boundary problems; Quasi-linear elliptic; Quasilinear elliptic equations; Hele-Shaw flow; non-local; implicit function theorem; Heterogeneous Multi Scale; HMM; Finite Element; FEM; FE; Mathematics; Matematik;

   Sammanfattning : This thesis is in the field of non-linear partial differential equations (PDE), focusing on problems which show some type of phase-transition. A single phase Hele-Shaw flow models a Newtoninan fluid which is being injected in the space between two narrowly separated parallel planes. LÄS MER

4. 3. Regularization methods for solving Cauchy problems for elliptic and degenerate elliptic equations

   Författare :Jennifer Chepkorir; Vladimir Kozlov; Fredrik Berntsson; Alexei Iantchenko; Linköpings universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES;

   Sammanfattning : In this thesis, we study Cauchy problems for the elliptic and degenerate elliptic equations. These problems are ill-posed. We split the boundary of the domain into two parts. On one of them, say Γ0, we have available Cauchy data and on remaining part Γ1 we introduce unknown Robin data. LÄS MER

5. 4. Convergence analysis of domain decomposition methods : Nonlinear elliptic and linear parabolic equations

   Författare :Emil Engström; Matematik LTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Nonoverlapping domain decomposition; Steklov--Poincaré operator; Robin--Robin method; Convergence; Nonlinear elliptic equation; Space-time;

   Sammanfattning : Domain decomposition methods are widely used tools for solving partial differential equations in parallel. However, despite their long history, there is a lack of rigorous convergence theory for equations with non-symmetric differential operators. This includes both nonlinear elliptic equations and linear parabolic equations. LÄS MER

7. 5. Numerical Complexity Analysis of Weak Approximation of Stochastic Differential Equations

   Författare :Raul Tempone Olariaga; KTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Adaptive methods; a posteriori error estimates; stochastic differential equations; weak approximation; Monte Carlo methods; Malliavin Calculus; HJM model; option price; bond market; stochastic elliptic equation; Karhunen-Loeve expansion; numerical co; Numerical analysis; Numerisk analys;

   Sammanfattning : The thesis consists of four papers on numerical complexityanalysis of weak approximation of ordinary and partialstochastic differential equations, including illustrativenumerical examples. Here by numerical complexity we mean thecomputational work needed by a numerical method to solve aproblem with a given accuracy. LÄS MER