Zobrazeno 1 - 10
of 246
pro vyhledávání: '"Helge Holden"'
Publikováno v:
Forum of Mathematics, Sigma, Vol 8 (2020)
We analyze stability of conservative solutions of the Cauchy problem on the line for the Camassa–Holm (CH) equation. Generically, the solutions of the CH equation develop singularities with steep gradients while preserving continuity of the solutio
Externí odkaz:
https://doaj.org/article/0224aba170aa43c18d077c923cf3e02f
Publikováno v:
Forum of Mathematics, Sigma, Vol 3 (2015)
We introduce a novel solution concept, denoted ${\it\alpha}$-dissipative solutions, that provides a continuous interpolation between conservative and dissipative solutions of the Cauchy problem for the two-component Camassa–Holm system on the line
Externí odkaz:
https://doaj.org/article/733dae69a97f46a7af77804b9a2ee8f4
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
We construct a Lipschitz metric for conservative solutions of the Cauchy problem on the line for the two-component Camassa--Holm system $u_t-u_{txx}+3uu_x-2u_xu_{xx}-uu_{xxx}+\rho\rho_x=0$, and $\rho_t+(u\rho)_x=0$ with given initial data $(u_0, \rho
Externí odkaz:
http://arxiv.org/abs/1306.6822
Soliton Equations and Their Algebro-Geometric Solutions: Volume 2, (1+1)-Dimensional Discrete Models
As a partner to Volume 1: Dimensional Continuous Models, this monograph provides a self-contained introduction to algebro-geometric solutions of completely integrable, nonlinear, partial differential-difference equations, also known as soliton equati
Autor:
Helge Holden
Publikováno v:
European Mathematical Society Magazine. :45-49
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d6c7de9d5219e38d99f0954426c0107e
https://doi.org/10.4171/mag/119
https://doi.org/10.4171/mag/119
Autor:
Fritz Gesztesy, Helge Holden
The focus of this book is on algebro-geometric solutions of completely integrable nonlinear partial differential equations in (1+1)-dimensions, also known as soliton equations. Explicitly treated integrable models include the KdV, AKNS, sine-Gordon,
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
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
Autor:
Helge Holden, Bernt Øksendal
Publikováno v:
Nonlinear Theory of Generalized Functions ISBN: 9780203745458
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::cdcd09744b7c6be76c25462224a5cb99
https://doi.org/10.1201/9780203745458-28
https://doi.org/10.1201/9780203745458-28