Well-posedness of boundary-value problems for multidimensional hyperbolic systems
By the method of characteristics, we investigate the well-posedness of local (the Cauchy problem, mixed problems) and nonlocal (with nonseparable and integral boundary conditions) problems for some multidimensional almost linear first-order hyperbolic systems. Reducing these problems to the systems of integral operator equations, we prove the existence and uniqueness of classical solutions.
English version (Springer): Ukrainian Mathematical Journal 60 (2008), no. 2, pp 221-234.
Citation Example: Kmit I. Ya., Ptashnik B. I. Well-posedness of boundary-value problems for multidimensional hyperbolic systems // Ukr. Mat. Zh. - 2008. - 60, № 2. - pp. 192–203.