Zobrazeno 1 - 10
of 127
pro vyhledávání: '"Nils Henrik Risebro"'
Publikováno v:
Nonlinearity. 34:1633-1662
In this paper we develop an existence theory for the nonlinear initial-boundary value problem with singular diffusion $\partial_t u = \text{div}(k(x)\nabla G(u))$, $u|_{t=0}=u_0$ with Neumann boundary conditions $k(x)\nabla G(u)\cdot \nu = 0$. Here $
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e5207cce483c1b4a65134a9e84710827
https://doi.org/10.1088/1361-6544/abde9d
https://doi.org/10.1088/1361-6544/abde9d
Autor:
Nils Henrik Risebro
Publikováno v:
Vietnam Journal of Mathematics. 47:835-849
We compare three different models of two phase flow in a porous medium; the standard Darcy/Buckley–Leverett model, the Brinkman model and the Helmholtz model. These three models are all singular perturbations of the inviscid Darcy model, and thus h
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::748776b20b6bc24ef71023f7179558ac
https://doi.org/10.1007/s10013-019-00367-1
https://doi.org/10.1007/s10013-019-00367-1
Publikováno v:
Stochastics and Partial Differential Equations: Analysis and Computations. 8:186-261
Finite volume methods are proposed for computing approximate pathwise entropy/kinetic solutions to conservation laws with a rough path dependent flux function. For a convex flux, it is demonstrated that rough path oscillations may lead to "cancellati
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3d065e58045921b700d7e705b6788eea
https://doi.org/10.1007/s40072-019-00145-7
https://doi.org/10.1007/s40072-019-00145-7
We consider nonlinear scalar conservation laws posed on a network. We define an entropy condition for scalar conservation laws on networks and establish $L^1$ stability, and thus uniqueness, for weak solutions satisfying the entropy condition. We app
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6961fbb90825de07b59f468b24038fbb
Publikováno v:
Journal of Differential Equations. 265:2708-2744
For scalar conservation laws driven by a rough path $z(t)$, in the sense of Lions, Perthame and Souganidis in arXiv:1309.1931, we show that it is possible to replace $z(t)$ by a piecewise linear path, and still obtain the same solution at a given tim
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::32592e5264ea8215ac6c2a825a70bc5f
https://doi.org/10.1016/j.jde.2018.04.045
https://doi.org/10.1016/j.jde.2018.04.045
We consider conservation laws with discontinuous flux where the initial datum, the flux function, and the discontinuous spatial dependency coefficient are subject to randomness. We establish a notion of random adapted entropy solutions to these equat
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bbba5f84ca7366a939b36191bce056bd
We analyze a model equation arising in option pricing. This model equation takes the form of a nonlinear, nonlocal diffusion equation. We prove the well posedness of the Cauchy problem for this equation. Furthermore, we introduce a semidiscrete diffe
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0ce4693064e2921e36d20b8b992ecc75
http://hdl.handle.net/11589/182382
http://hdl.handle.net/11589/182382
Autor:
Nils Henrik Risebro, Helge Holden
Publikováno v:
SIAM Journal on Mathematical Analysis
We study vehicular traffic on a road with multiple lanes and dense, unidirectional traffic following the traditional Lighthill--Whitham--Richards model where the velocity in each lane depends only on the density in the same lane. The model assumes th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8b5b46adfab41ddb3e4a355d655c44f3
http://hdl.handle.net/11250/2633052
http://hdl.handle.net/11250/2633052
Publikováno v:
BIT Numerical Mathematics. 57:93-122
We prove the convergence of a finite difference scheme to the unique entropy solution of a general form of the Ostrovsky-Hunter equation on a bounded domain with periodic boundary conditions. The equation models, for example, shallow water waves in a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bc4f4b76f6347d3697506b497cf64b63
https://doi.org/10.1007/s10543-016-0625-x
https://doi.org/10.1007/s10543-016-0625-x
Publikováno v:
ESAIM: Mathematical Modelling and Numerical Analysis. 50:499-539
We analyze upwind difference methods for strongly degenerate convection-diffusion equations in several spatial dimensions. We prove that the local L 1 -error between the exact and numerical solutions is 𝓞( Δx 2 / (19 + d ) ), where d is the spati
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e434d8238b5d4f30c6afe60f96f8f35a
https://doi.org/10.1051/m2an/2015057
https://doi.org/10.1051/m2an/2015057