半无界区域上算子L_q=~2/(t^2)-~2/(x^2)+q(t)的反问题

讨论半无界区域上如下双曲方程确定函数偶（ｕ，ｑ）的反问题：ｕｔ－ｕｘｘ＋ｑ（ｔ）ｕ＝Ｆ（ｘ，ｔ），ｘ＞０，ｔ＞０，ｕ（ｘ，０）＝φ（ｘ），ｕｔ（ｘ，０）＝ψ（ｘ），ｘ≥０，ｕ（０，ｔ）＝ｆ（ｔ），ｔ≥０，ｕｘ（０，ｔ）＝ｇ（ｔ），ｔ≥０．给出了局部解的存在性、唯一性和稳定性结果．

NONLINEAR HYPERBOLIC CAUCHY PROBLEMS IN GEVREY CLASSES

The authors prove well posedness in Gevrey classes of Cauchy problem for nonlinear hyper- bolic equations of constant multiplicity with Holder dependence on the time variable.

ＯＮＴＨＥＨＹＰＥＲＢＯＬＩＣＯＢＳＴＡＣＬＥ ＰＲＯＢＬＥＭＯＦＦＩＲＳＴＯＲＤＥＲ

This paper presents new results for strong solutions and their coincidence sets of the obstacle problem for linear hyperbolic operators of first order. An inequality similar to the LewyStampacchia ones for elliptic and parabolic problems is shown. Under nondegeneracy conditions the stability of the coincidence set is shown with respect to the variation of the data and with respect to approximation by semilinear hyperbolic problems. These results are applied to the asymptotic stability of the evolution problem with respect to the stationary coercive problem with obstacle.