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Shock Waves in Plane Symmetric Spacetimes
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering and Sustainable Development.
2008 (English)In: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 33, no 11, p. 2020-2039Article in journal (Refereed) Published
Abstract [en]

We consider Einstein's equations coupled to the Euler equations in plane symmetry, with compact spatial slices and constant mean curvature time. We show that for a wide variety of equations of state and a large class of initial data, classical solutions break down in finite time. The key mathematical result is a new theorem on the breakdown of solutions of systems of balance laws. We also show that an extension of the solution is possible if the spatial derivatives of the energy density and the velocity are bounded, indicating that the breakdown is really due to the formation of shock waves.

Place, publisher, year, edition, pages
2008. Vol. 33, no 11, p. 2020-2039
National Category
Mathematics Natural Sciences
Identifiers
URN: urn:nbn:se:miun:diva-8302DOI: 10.1080/03605300802421948ISI: 000260833800005Scopus ID: 2-s2.0-56049117658OAI: oai:DiVA.org:miun-8302DiVA, id: diva2:134134
Note
VR-MathematicsAvailable from: 2009-01-18 Created: 2009-01-18 Last updated: 2017-12-14Bibliographically approved

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Ståhl, Fredrik

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