Zobrazeno 1 - 10
of 90
pro vyhledávání: '"Michael Kunzinger"'
Publikováno v:
Electronic Journal of Differential Equations, Vol 2005, Iss 01, Pp 1-17 (2005)
We consider a collisionless ensemble of classical particles coupled with a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, the relativistic Vlasov-Klein-Gordon system, we prove local-in-time existence of clas
Externí odkaz:
https://doaj.org/article/0957c17078464ab1b2b9d3969ffb0fa7
Autor:
Michael Kunzinger, Roland Steinbauer
Publikováno v:
Annales Henri Poincaré. 23:4319-4342
The null distance of Sormani and Vega encodes the manifold topology as well as the causality structure of a (smooth) spacetime. We extend this concept to Lorentzian length spaces, the analog of (metric) length spaces, which generalize Lorentzian caus
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ee22047da6ed716d12a0a99942551a86
https://doi.org/10.1007/s00023-022-01198-6
https://doi.org/10.1007/s00023-022-01198-6
We prove existence of weak solutions to the Cauchy problem corresponding to various strictly parabolic equations on a compact Riemannian manifold $(M,g)$. This also includes strictly parabolic equations with stochastic forcing with linear diffusion.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::05b611f81d89136d17c7f85de3b41dd1
We extend both the Hawking-Penrose Theorem and its generalisation due to Galloway and Senovilla to Lorentzian metrics of regularity $C^1$. For metrics of such low regularity, two main obstacles have to be addressed. On the one hand, the Ricci tensor
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7f18f08af235d0d762f56b0426bc323c
https://phaidra.univie.ac.at/o:1624664
https://phaidra.univie.ac.at/o:1624664
Publikováno v:
Annals of Global Analysis and Geometry
We study the low-regularity (in-)extendibility of spacetimes within the synthetic-geometric framework of Lorentzian length spaces developed in [KS:17]. To this end, we introduce appropriate notions of geodesics and timelike geodesic completeness and
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9343bb390098182424349a658b52a05c
http://europepmc.org/articles/PMC6397613
http://europepmc.org/articles/PMC6397613
Questions regarding the interplay of nonlinearity and the creation and propagation of singularities arise in a variety of fields-including nonlinear partial differential equations, noise-driven stochastic partial differential equations, general relat
Publikováno v:
University of Vienna-u:cris
We consider the degenerate parabolic equation $$ \partial_t u +\mathrm{div} {\mathfrak f}_{\bf x}(u)=\mathrm{div}(\mathrm{div} ( A_{\bf x}(u) ) ), \ \ {\bf x} \in M, \ \ t\geq 0 $$ on a smooth, compact, $d$-dimensional Riemannian manifold $(M,g)$. He
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2dd010ce2b3e68b831e186aafd33d0c2
https://doi.org/10.1016/j.jde.2017.06.001
https://doi.org/10.1016/j.jde.2017.06.001
The well-known solution theory for (systems of) linear ordinary differential equations undergoes significant changes when introducing an additional real parameter. Properties like the existence of fundamental sets of solutions or characterizations of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6745b040fdf81c4aa20d23993f28745b
We present two new proofs of the exchange theorem for the Laplace transformation of vector-valued distributions. We then derive an explicit solution to the Dirichlet problem of the polyharmonic operator in a half-space. Finally, we obtain explicit so
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1c3147c26ee8d901050fbb65693007d3
http://arxiv.org/abs/1809.10444
http://arxiv.org/abs/1809.10444
Publikováno v:
Zeitschrift Fuer Angewandte Mathematik Und Physik
We prove existence and uniqueness of a solution to the Cauchy problem corresponding to the equation \begin{equation*} \begin{cases} \partial_t u_{\varepsilon,\delta} +\mathrm{div} {\mathfrak f}_{\varepsilon,\delta}({\bf x}, u_{\varepsilon,\delta})=\v
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a17b8ed3647d031d023d11a6c4a31a29
http://arxiv.org/abs/1805.02723
http://arxiv.org/abs/1805.02723