Global well-posedness of a class of singular hyperbolic Cauchy problems

DOI10.1007/S00605-022-01723-ZOpenAlexW4281907912WikidataQ115606398 ScholiaQ115606398MaRDI QIDQ2684474

N. Uday Kiran, Rahul Raju Pattar

Publication date: 16 February 2023

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.09927

zbMATH Keywords

second orderunbounded coefficientswell-posedness of the Cauchy problemlinear hyperbolic equationsloss of regularity

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Pseudodifferential operators as generalizations of partial differential operators (35S05) Initial value problems for second-order hyperbolic equations (35L15) Singular hyperbolic equations (35L81)

Cites Work

• Microlocal analysis for waves propagating in Einstein \& de Sitter spacetime
• The Cauchy problem for strictly hyperbolic operators with non-absolutely continuous coefficients.
• Global well-posedness of a class of strictly hyperbolic Cauchy problems with coefficients non-absolutely continuous in time
• Energy estimates and global well-posedness for a broad class of strictly hyperbolic Cauchy problems with coefficients singular in time
• Strictly hyperbolic Cauchy problems on \(\mathbb{R}^n\) with unbounded and singular coefficients
• Hölder continuity in time for SG hyperbolic systems
• Loss of regularity for the solutions to hyperbolic equations with non-regular coefficients?an application to Kirchhoff equation
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