Zobrazeno 1 - 10
of 31
pro vyhledávání: '"KATRIN GRUNERT"'
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
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
Publikováno v:
Communications in Partial Differential Equations
This paper provides an asymptotic description of a solution to the Burgers-Hilbert equation in a neighborhood of a point where two shocks interact. The solution is obtained as the sum of a function with $H^2$ regularity away from the shocks plus a co
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::19f2fb8697a38dd701dbdec96e994450
Autor:
Katrin Grunert, Helge Holden
Publikováno v:
Research in the Mathematical Sciences
We show that the Hunter-Saxton equation $u_t+uu_x=\frac14\big(\int_{-\infty}^x d\mu(t,z)- \int^{\infty}_x d\mu(t,z)\big)$ and $\mu_t+(u\mu)_x=0$ has a unique, global, weak, and conservative solution $(u,\mu)$ of the Cauchy problem on the line.
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Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cc49bfd0ff50d697ffe9f0fa9528874f
http://arxiv.org/abs/2107.12681
http://arxiv.org/abs/2107.12681
Publikováno v:
Proceedings of the National Academy of Sciences. 118
To demonstrate the existence of an evolutionarily stable strategy (ESS) in fluctuating ecological systems (such as predator−prey system with limit cycles) is important. Deriving the analytic conditions for such an ESS can be of great help when stud
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::945162ff27d84dccf8a888a8c57833af
https://doi.org/10.1073/pnas.2102861118
https://doi.org/10.1073/pnas.2102861118
Autor:
Audun Reigstad, Katrin Grunert
Publikováno v:
SN Partial Differential Equations and Applications (SN PDE)
We study traveling wave solutions of the nonlinear variational wave equation. In particular, we show how to obtain global, bounded, weak traveling wave solutions from local, classical ones. The resulting waves consist of monotone and constant segment
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::81d4526c07bff18e05146b87e031c11c
https://hdl.handle.net/11250/2984072
https://hdl.handle.net/11250/2984072
Publikováno v:
BIT Numerical Mathematics
In the article a convergent numerical method for conservative solutions of the Hunter–Saxton equation is derived. The method is based on piecewise linear projections, followed by evolution along characteristics where the time step is chosen in orde
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0dfd69574d087ea5c599b6097b677489
https://hdl.handle.net/11250/2756401
https://hdl.handle.net/11250/2756401
Autor:
Katrin Grunert, Matthew Tandy
Publikováno v:
Journal of Hyperbolic Differential Equations
We study the Lipschitz stability in time for $\alpha$-dissipative solutions to the Hunter-Saxton equation, where $\alpha \in [0,1]$ is a constant. We define metrics in both Lagrangian and Eulerian coordinates, and establish Lipschitz stability for th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fe0867a4c23b590dad6fc28556d76e5c