Browsing NTNU Open by Author "Endal, Jørgen"
Now showing items 1-15 of 15
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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 non-Brownian tug-of-war game. We first ... -
L1 contraction for bounded (nonintegrable) solutions of degenerate parabolic equations
Endal, Jørgen; Jakobsen, Espen Robstad (Journal article; Peer reviewed, 2014-12-11)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 ... -
Large-time behaviour for anisotropic stable nonlocal diffusion problems with convection
Endal, Jørgen; Ignat, Liviu I.; Quirós, Fernando (Journal article; Peer reviewed, 2023)We study the large-time behaviour of nonnegative solutions to the Cauchy problem for a nonlocal heat equation with a nonlinear convection term. The diffusion operator is the infinitesimal generator of a stable Lévy process, ... -
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) ... -
Nonlinear fractional convection-diffusion equations, with nonlocal and nonlinear fractional diffusion
Endal, Jørgen (Master thesis, 2013)We study nonlinear fractional convection-diffusion 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 well-posedness ... -
Nonlocal nonlinear diffusion equations. Smoothing effects, Green functions, and functional inequalities
Bonforte, Matteo; Endal, Jørgen (Peer reviewed; Journal article, 2023)We establish boundedness estimates for solutions of generalized porous medium equations of the form where and is a linear, symmetric, and nonnegative operator. The wide class of operators we consider includes, but is not ... -
On Degenerate Parabolic Problems with Local and Nonlocal Diffusion
Endal, Jørgen (Doctoral theses at NTNU;2017:229, Doctoral thesis, 2017) -
On distributional solutions of local and nonlocal problems of porous medium type
del Teso Mendez, Felix; Endal, Jørgen; Jakobsen, Espen Robstad (Journal article; Peer reviewed, 2017)We present a theory of well-posedness and a priori estimates for bounded distributional (or very weak) solutions of ∂tu − L σ,µ[ϕ(u)] = g(x, t) in R N (0.1) × (0, T ), where ϕ is merely continuous and nondecreasing and L ... -
On the two-phase fractional Stefan problem
Endal, Jørgen; del Teso, Félix; Vázquez, Juan Luis (Journal article; Peer reviewed, 2020) -
On the well-posedness of solutions with finite energy for nonlocal equations of porous medium type
del Teso, Félix; Endal, Jørgen; Jakobsen, Espen Robstad (Chapter, 2018)We study well-posedness and equivalence of different notions of solutions with finite energy for nonlocal porous medium type equations of the form ∂tu − Aϕ(u) = 0. These equations are possibly degenerate nonlinear diffusion ... -
Robust numerical methods for nonlocal (and local) equations of porous medium type. Part I: Theory
Teso, Felix del; Endal, Jørgen; Jakobsen, Espen Robstad (Journal article; Peer reviewed, 2019)We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $\partial_t u-\mathfrak{L}^{\sigma,\mu}[\varphi(u)]=f \;\text{in}\; \mathbb{R}^ ... -
Robust numerical methods for nonlocal (and local) equations of porous medium type. Part II: Schemes and experiments
del Teso, Félix; Endal, Jørgen; Jakobsen, Espen Robstad (Journal article; Peer reviewed, 2018)We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $\partial_t u-\mathfrak{L}[\varphi(u)]=f(x,t)$ in $\mathbb{R}^N\times(0,T),$ where ... -
Uniform tail estimates and Lp(RN)-convergence for finite-difference approximations of nonlinear diffusion equations
del Teso, Félix; Endal, Jørgen; Jakobsen, Espen Robstad (Journal article; Peer reviewed, 2022) -
Uniqueness and properties of distributional solutions of nonlocal equations of porous medium type
del Teso, Félix; Endal, Jørgen; Jakobsen, Espen Robstad (Journal article; Peer reviewed, 2017)We study the uniqueness, existence, and properties of bounded distributional solutions of the initial value problem for the anomalous diffusion equation ∂tu−Lμ[φ(u)]=0. Here Lμ can be any nonlocal symmetric degenerate ...