| dc.contributor.advisor | Witt, Ingo Prof. Dr. | |
| dc.contributor.author | Krüger, Matthias | |
| dc.date.accessioned | 2018-08-31T09:48:02Z | |
| dc.date.available | 2018-08-31T09:48:02Z | |
| dc.date.issued | 2018-08-31 | |
| dc.identifier.uri | http://hdl.handle.net/11858/00-1735-0000-002E-E491-C | |
| dc.identifier.uri | http://dx.doi.org/10.53846/goediss-7038 | |
| dc.language.iso | eng | de |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject.ddc | 510 | de |
| dc.title | On the Cauchy problem for a class of degenerate hyperbolic equations | de |
| dc.type | doctoralThesis | de |
| dc.contributor.referee | Witt, Ingo Prof. Dr. | |
| dc.date.examination | 2018-05-18 | |
| dc.description.abstracteng | In this thesis, a pseudodifferential calculus for a degenerate hyperbolic Cauchy
problem is developed. The model for this problem originates from a certain observation
in fluid mechanics, and is then extended to a more general class of hyperbolic
Cauchy problems where the coefficients degenerate like a power of $t + |x|^2$ as
$(t,x) \to (0,0)$.
Symbol classes and pseudodifferential operators are introduced. In this process,
it becomes apparent that exactly in the origin, these operators are of type (1,1).
Although these operators are not $L^2$-continuous in general, a proof of continuity in
$\mathscr C([0,T],L^2(\mathbb R^d))$ is given for a suitable subclass.
An adapted scale of function spaces is defined, where at $t = 0$ these spaces coincide
with 2-microlocal Sobolev spaces with respect to the Lagrangian $\dot T^*_0\mathbb R^d$. In these
spaces, energy estimates are derived, so that a symbolic approach can be applied to
prove wellposedness of the Cauchy problem. | de |
| dc.contributor.coReferee | Bahns, Dorothea Prof. Dr. | |
| dc.subject.eng | degenerate hyperbolic Cauchy problem | de |
| dc.subject.eng | partial differential equations | de |
| dc.subject.eng | pseudodifferential operators | de |
| dc.identifier.urn | urn:nbn:de:gbv:7-11858/00-1735-0000-002E-E491-C-0 | |
| dc.affiliation.institute | Fakultät für Mathematik und Informatik | de |
| dc.subject.gokfull | Mathematics (PPN61756535X) | de |
| dc.identifier.ppn | 103040657X | |