A Problem with Condition Containing an Integral Term for a Parabolic-Hyperbolic Equation
AbstractIn a layer obtained as the Cartesian product of an interval $[−T_1 ,T_2], T_1 ,T_2 > 0$, and a space $ℝ_p, p ≥ 1$, we study a problem with nonlocal condition in the time variable containing an integral term for a mixed parabolic-hyperbolic equation in the class of functions almost periodic in the space variables. For this problem, we establish a criterion of uniqueness and sufficient conditions for the existence of solutions. To solve the problem of small denominators encountered in the construction of the solution, we use the metric approach.
How to Cite
Kuz, A. M., and B. I. Ptashnik. “A Problem With Condition Containing an Integral Term for a Parabolic-Hyperbolic Equation”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 5, May 2015, pp. 635-44, http://umj.imath.kiev.ua/index.php/umj/article/view/2011.