Browsing NTNU Open by Author "Jakobsen, Espen Robstad"
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A spectral method for fractional porous medium equations
Bærland, Trygve (Master thesis, 2015)This master's thesis considers the fractional general porous medium equation; a nonlocal equation with nonlinear diffusivity. Properties of the nonlocal operator are derived. Existence of distributional solutions are proved, ... 
Analysis and discretization of fractional Mean Field Games
Ersland, Olav (Doctoral theses at NTNU;2021:399, Doctoral thesis, 2021) 
Deep Learning Algorithms for Solving PDEs  Presentation and Implementation of Deep Learning Algorithms for Solving SemiLinear Parabolic PDEs with an Extension to the Fractional Laplace Operator
Ameln, Oscar Christian (Master thesis, 2020)I juni 2017 presenterer Weinan E, Jiequn Han og Arnulf Jentzen en banebrytende algoritme, Deep Backward Stochastic Differential Equation (Deep BSDE), for å løse partielle differensiallikninger (PDEer) ved bruk av dyp læring. ... 
Discontinous Galerkin Methods for Conservation Laws,  with and without fractional diffusion
Sigurdsson, Alexander N. (Master thesis, 2018)This thesis was submitted on July 5'th 2018 as the Master's thesis for Alexander N Sigurdsson in Industrial Mathematics at the Department of Mathematical Sciences at The Norwegian University of Science and Technology (NTNU). ... 
Evolution driven by the infinity fractional Laplacian
del Teso, Félix; Endal, Jørgen; Jakobsen, Espen Robstad; Vázquez, Juan Luis (Peer reviewed; Journal article, 2023)We consider the evolution problem associated to the infinity fractional Laplacian introduced by Bjorland et al. (Adv Math 230(4–6):1859–1894, 2012) as the infinitesimal generator of a nonBrownian tugofwar game. We first ... 
Evolutionarily stable strategies in stable and periodically fluctuating populations: The Rosenzweig–MacArthur predator–prey model
Grunert, Katrin; Holden, Helge; Jakobsen, Espen Robstad; Stenseth, Nils Christian (Peer reviewed; Journal article, 2021)An evolutionarily stable strategy (ESS) is an evolutionary strategy that, if adapted by a population, cannot be invaded by any deviating (mutant) strategy. The concept of ESS has been extensively studied and widely applied ... 
Existence, smoothness and numerical approximation for two generalizations of the stochastic heat equation
Furset, Simen Knutsen (Master thesis, 2023)I denne avhandlingen ser jeg på to klasser av stokastiske evolusjonsligninger. Jeg ser på eksistens og unikhetsresultater for svake løsninger og jeg ser på resultater som beskriver glattheten og kovariansegenskapene til ... 
Improved order 1/4 convergence for piecewise constant policy approximation of stochastic control problems
Jakobsen, Espen Robstad; Picarelli, Athena; Reisinger, Christoph (Journal article; Peer reviewed, 2019)In N. V. Krylov, Approximating value functions for controlled degenerate diffusion processes by using piecewise constant policies, Electron. J. Probab., 4(2), 1999, it is proved under standard assumptions that the value ... 
L1 contraction for bounded (nonintegrable) solutions of degenerate parabolic equations
Endal, Jørgen; Jakobsen, Espen Robstad (Journal article; Peer reviewed, 20141211)We obtain new L1 contraction results for bounded entropy solutions of Cauchy problems for degenerate parabolic equations. The equations we consider have possibly strongly degenerate local or nonlocal diffusion terms. As ... 
L1 semigroup generation for FokkerPlanck operators associated with general Levy driven SDEs
Chen, Linghua; Jakobsen, Espen Robstad (Journal article; Peer reviewed, 2018)We prove a new generation result in L 1 for a large class of nonlocal operators with nondegenerate local terms. This class contains the operators appearing in FokkerPlanck or Kolmogorov forward equations associated ... 
The Liouville theorem and linear operators satisfying the maximum principle.
Alibaud, Nathael; del Teso, Félix; Endal, Jørgen; Jakobsen, Espen Robstad (Peer reviewed; Journal article, 2020)A result by Courrège says that linear translation invariant operators satisfy the maximum principle if and only if they are of the form L = Lσ,b + Lμ where Lσ,b[u](x) = tr(σσTD2u(x)) + b · Du(x) and Lμ[u](x) = Rd\{0} u(x ... 
The Liouville theorem and linear operators satisfying the maximum principle.
Alibaud, Nathael; del Teso, Félix; Endal, Jørgen; Jakobsen, Espen Robstad (Peer reviewed; Journal article, 2020)A result by Courrège says that linear translation invariant operators satisfy the maximum principle if and only if they are of the form L = Lσ,b + Lμ where Lσ,b[u](x) = tr(σσTD2u(x)) + b · Du(x) and Lμ[u](x) ... 
Maximum Principles for Differential Equations
Duguma, Tadesse Guluma (Master thesis, 2014)maximum principle is one among the most useful and best known tools used in the study of partial differential equations. This principle is a generalization of the well known fact of calculus that any function u(x) which ... 
Nonlinear fractional convectiondiffusion equations, with nonlocal and nonlinear fractional diffusion
Endal, Jørgen (Master thesis, 2013)We study nonlinear fractional convectiondiffusion equations with nonlocal and nonlinear fractional diffusion. By the idea of Kru\v{z}kov (1970), entropy sub and supersolutions are defined in order to prove wellposedness ... 
Nonlinear integrodifferential Equations: Numerical Solutions by using Spectral Methods
Davidsen, SteinOlav Hagen (Master thesis, 2013)This article deals with numerical solutions of nonlinear integrodifferential convectiondiffusion equations using spectral methods. More specifically, the spectral vanishing viscosity method is introduced and analyzed to ... 
Numerical Methods and Brute Force Optimisation for a General Formulation of the Mean Field Game Equations
Husby, Snorre Alexander Berthelsen (Master thesis, 2015)This thesis considers the numerical solution of a general formulation of the mean field game (MFG) equations. MFG are a relatively new field with few general results but with many modelling applications. The MFG equations ... 
Numerical Methods for Valuation and Optimal Operation of Natural Gas Storage
Følstad, Erik Magnus G. (Master thesis, 2015)The thesis describes different approaches for solving numerically a PDE model for the valuation and optimal operation of a natural gas storage facility, characterized as a Hamilton Jacobi Bellman (HJB) equation. The HJB ... 
Numerical Models for Jump Diffusion Processes: A Finite Element Approach
Hornæs, Kristin Kaarbø (Master thesis, 2013)In this thesis we propose a finite element solution to the jump diffusion problem for pricing options. We focus on assets following CGMY processes and formulate the problem in weak bilinear form. In the case where the CGMY ... 
Numericsinformed neural networks and inverse problems with hyperbolic balance laws
Waade, Bendik Skundberg (Master thesis, 2023)Vi introduserer numerikkbevisste nevrale nettverk (NINN), et rammeverk utviklet for å lære kildeledd i hyperbolske partielle differensialligninger. NINN kombinerer klassiske numeriske metoder med nevrale nettverk for å ... 
On Degenerate Parabolic Problems with Local and Nonlocal Diffusion
Endal, Jørgen (Doctoral theses at NTNU;2017:229, Doctoral thesis, 2017)