Sökning: "nonlinear PDEs"

Visar resultat 1 - 5 av 10 avhandlingar innehållade orden nonlinear PDEs.

1. 1. 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

3. 2. Painlevé analysis and transformations for nonlinear partial differential equations

   Författare :Ove Lindblom; Luleå tekniska universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematics; Matematik;

   Sammanfattning : Nonlinear partial differential equations play a fundamental role in the description of many physical models. In order to get a complete understanding of the phenomena which are modeled it is important to obtain exact analytic solutions. LÄS MER

4. 3. Conservation Laws, Numerical Schemes and Control Strategies for Sedimentation and Wastewater Treatment

   Författare :Sebastian Farås; Matematik LTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Conservation law; Temple class system; numerical scheme; continuous sedimentation;

   Sammanfattning : A consistent theme throughout this thesis is quasilinear partial differential equations (PDEs) appearing in one-dimensional models of sedimentation for solid-liquid separation of suspensions. We mainly focus on continuous sedimentation in so-called clarifier-thickeners (CTs), which are found in mineral processing and wastewater treatment. LÄS MER

5. 4. Oversampled radial basis function methods for solving partial differential equations

   Författare :Igor Tominec; Elisabeth Larsson; Bengt Fornberg; Uppsala universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; radial basis function; PDE; oversampling; stability; RBF-FD; RBF-PUM; unfitted;

   Sammanfattning : Partial differential equations (PDEs) describe complex real-world phenomena such as weather dynamics,  object deformations, financial trading prices, and fluid-structure interaction.  The solutions of PDEs are commonly used to enhance the understanding of these phenomena and also as leverage to make technological improvements to consumer products. LÄS MER

7. 5. Selected Topics in Mathematical Modelling: Machine Learning and Tugs-of-War

   Författare :Carmina Fjellström; Kaj Nyström; Andrea Pascucci; Uppsala universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Machine learning; Neural networks; LSTM; Financial forecasting; Time series analysis; Stochastic gradient descent; Diffusion map; Dimension reduction; Tug-of-war games; Fractional heat operator; Mean value property; Infinity fractional heat operators; Dynamic programming principle; p-Laplacian; Infinity Laplacian; Kolmogorov equation; Stochastic games; Viscosity solutions; Tillämpad matematik och statistik; Applied Mathematics and Statistics;

   Sammanfattning : This thesis concerns selected topics in mathematical modelling, namely in machine learning and stochastic games called tugs-of-war. It consists of four scientific articles. The first and second are about machine learning topics, while the third and fourth articles are about tug-of-war games. LÄS MER