A Problem with Condition Containing an Integral Term for a Parabolic-Hyperbolic Equation
In 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.
English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 5, pp 723-734.
Citation Example: Kuz A. M., Ptashnik B. I. A Problem with Condition Containing an Integral Term for a Parabolic-Hyperbolic Equation // Ukr. Mat. Zh. - 2015. - 67, № 5. - pp. 635-644.