Sökning: "Nonlinear elliptic equation"

Visar resultat 1 - 5 av 14 avhandlingar innehållade orden Nonlinear elliptic equation.

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. 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

4. 3. 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

5. 4. Nonlinear elliptic problems with boundary blow-up

   Författare :Jerk Matero; Uppsala universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematics; Boundary blow-up; NTA domain; fractal; p-Laplaceoperator; Mange-Ampère operator; viscosity solution; mean curvature flow; gradient estimate; Fefferman s equation; superdiffusion; entire solution; maximum principle; Primary 35J65; MATEMATIK; MATHEMATICS; MATEMATIK; matematik; Mathematics;

   Sammanfattning : A classical problem in differential geometry is the prescribed curvature problemin a bounded domain, where the task is to conformally deform the Euclidean metric to another complete Riemannian metric with a prescribed curvature function.If this function is negative, the problem is equivalent to solving a nonlinear elliptic partial differential equation with boundary blow-up. LÄS MER

7. 5. On some Nonlinear Aspects of Wave Motion

   Författare :Erik Wahlén; Partiella differentialekvationer; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; water waves; bifurcation; global existence; rod equation; wabve breaking;

   Sammanfattning : In the first part of this thesis we consider the governing equations for capillary water waves given by the Euler equations with a free surface under the influence of surface tension over a flat bottom. We look for two-dimensional steady periodic waves. The problem is first transformed to a nonlinear elliptic equation in a rectangle. LÄS MER