Well-posedness of many-dimensional Darboux problems for degenerating hyperbolic equations
Abstract
Forthe equation m∑i=ttkiUxi,xi−Un+m∑i=tai(x,t)Uxi+b(x,t)ut+c(x,t)u=0, ki=const≥0,i=l.....m,x=(x1,...,xm),m>2, we find a many-dimensional analog of the well-known "Gellerstedt condition" ai(x,t)=O(1)tα,i=1,...,m,α>k12−2. We prove that if this condition is satisfied, then the Darboux problems are uniquely solvable.
Published
25.10.1994
How to Cite
Aldashev, S. A. “Well-Posedness of Many-Dimensional Darboux Problems for Degenerating Hyperbolic Equations”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 46, no. 10, Oct. 1994, pp. 1304–1311, https://umj.imath.kiev.ua/index.php/umj/article/view/5607.
Issue
Section
Research articles