Zobrazeno 1 - 10
of 173
pro vyhledávání: '"Kenneth H. Karlsen"'
Autor:
Kenneth H. Karlsen, Suleyman Ulusoy
Publikováno v:
Electronic Journal of Differential Equations, Vol 2011, Iss 116,, Pp 1-23 (2011)
We analyze entropy solutions for a class of Levy mixed hyperbolic-parabolic equations containing a non-local (or fractional) diffusion operator originating from a pure jump Levy process. For these solutions we establish uniqueness (L^1 contraction pr
Externí odkaz:
https://doaj.org/article/355dedf4777c42b895e4e82898c1944f
Autor:
Mostafa Bendahmane, Kenneth H. Karlsen
Publikováno v:
Electronic Journal of Differential Equations, Vol 2006, Iss 46, Pp 1-30 (2006)
We prove existence results for distributional solutions of anisotropic nonlinear elliptic systems with a measure valued right-hand side. The functional setting involves anisotropic Sobolev spaces as well as weak Lebesgue (Marcinkiewicz) spaces. In a
Externí odkaz:
https://doaj.org/article/c1c82526c6c748fb92c5a9f0b74fb421
Publikováno v:
Electronic Journal of Differential Equations, Vol 2003, Iss 46, Pp 1-31 (2003)
We prove existence and uniqueness of entropy solutions for the Cauchy problem of weakly coupled systems of nonlinear degenerate parabolic equations. We prove existence of an entropy solution by demonstrating that the Engquist-Osher finite difference
Externí odkaz:
https://doaj.org/article/14cf9b1128484096bb00095d64fcadfe
Publikováno v:
Electronic Journal of Differential Equations, Vol 2002, Iss 93, Pp 1-23 (2002)
We study the Cauchy problem for the nonlinear (possibly strongly) degenerate parabolic transport-diffusion equation $$ partial_t u + partial_x (gamma(x)f(u))=partial_x^2 A(u), quad A'(cdot)ge 0, $$ where the coefficient $gamma(x)$ is possibly discont
Externí odkaz:
https://doaj.org/article/754a44d644bf43219ccf6b3066a9e419
Autor:
Espen R. Jakobsen, Kenneth H. Karlsen
Publikováno v:
Electronic Journal of Differential Equations, Vol 2002, Iss 39, Pp 1-10 (2002)
Using the maximum principle for semicontinuous functions [3,4], we prove a general ``continuous dependence on the nonlinearities'' estimate for bounded Holder continuous viscosity solutions of fully nonlinear degenerate elliptic equations. Furthermor
Externí odkaz:
https://doaj.org/article/1cc4d13ba0254e05b40a830f07d3b815
Publikováno v:
Journal of Differential Equations
In this paper we develop an existence theory for the Cauchy problem to the stochastic Hunter–Saxton equation (1.1) , and prove several properties of the blow-up of its solutions. An important part of the paper is the continuation of solutions to th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5b76d0038e0c809d6965951ee4919b15
https://doi.org/10.1016/j.jde.2020.07.031
https://doi.org/10.1016/j.jde.2020.07.031
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
Publikováno v:
Stochastic Processes and their Applications
We present a well-posedness result for strong solutions of one-dimensional stochastic differential equations (SDEs) of the form $$\mathrm{d} X= u(\omega,t,X)\, \mathrm{d} t + \frac12 \sigma(\omega,t,X)\sigma'(\omega,t,X)\,\mathrm{d} t + \sigma(\omega
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c3ca3c73d29c60db8b2f950c668e162a
Autor:
Luca Galimberti, Kenneth H. Karlsen
Publikováno v:
Stochastic Processes and their Applications
We consider the initial-value problem for stochastic continuity equations of the form ∂ t ρ + div h ρ u ( t , x ) + ∑ i = 1 N a i ( x ) ∘ d W i d t = 0 , defined on a smooth closed Riemannian manifold M with metric h , where the Sobolev regul
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::54e03804dba04255b23e90f1f83ac269
http://hdl.handle.net/10852/92317
http://hdl.handle.net/10852/92317
We consider the generalized almost periodic homogenization problem for two different types of stochastic conservation laws with oscillatory coefficients and multiplicative noise. In both cases the stochastic perturbations are such that the equation a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::89c186391c7857ef15cfa9ece6fa95bb
http://arxiv.org/abs/2006.02045
http://arxiv.org/abs/2006.02045