Abstract
For the wave equation we study boundary value problems, which are four-dimensional analogues of Darboux problems on the plane. It is shown that for n in ℕ there exists a right hand side smooth function from C n , for which the corresponding unique generalized solution has a strong power-type singularity at the point O. This singularity is isolated at the vertex O of the characteristic cone and does not propagate along the cone. The present article describes the exact behavior of the singular solutions at the point O. We give some necessary and sufficient conditions for existence of solutions with fixed order of singularity. It states some exact a priori estimates for the singular solutions
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
