Abstract
In this work a unique solvability of a class of hyperbolic type partial differential equations with unbounded coefficients is proved in \(\mathbb {R}^2\). The estimates of the weight norms of the solution u and its partial derivatives \(u_x\) and \(u_y\) are derived.
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This publication is supported by the target program 0085/PTSF-14 from the Ministry of Science and Education of the Republic of Kazakhstan.
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Muratbekov, M.B., Muratbekov, M.M., Dadaeva, A.N. (2017). A Sturm-Liouville Operator with a Negative Parameter and Its Applications to the Study of Differential Properties of Solutions for a Class of Hyperbolic Type Equations. In: Kalmenov, T., Nursultanov, E., Ruzhansky, M., Sadybekov, M. (eds) Functional Analysis in Interdisciplinary Applications. FAIA 2017. Springer Proceedings in Mathematics & Statistics, vol 216. Springer, Cham. https://doi.org/10.1007/978-3-319-67053-9_24
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