Nonlocal boundary-value problems for systems on linear partial differential equations
- 19 Downloads
We study the classical well-posedness of problems with nonlocal two-point conditions for typeless systems of linear partial differential equations with variable coefficients in a cylindrical domain. We prove metric theorems on lower bounds for small denominators that appear in the construction of solutions of such problems.
KeywordsHyperbolic System Nonlocal Condition Linear Partial Differential Equation Nonlocal Boundary Condition Small Denominator
Unable to display preview. Download preview PDF.
- 6.I. Ya. Kmit’, “On one problem with nonlocal time conditions for systems of hyperbolic type,” Mat. Met. Fiz.-Mekh. Polya, 37, 21–25 (1994).Google Scholar
- 11.T. I. Kiguradze, “On one boundary-value problem for hyperbolic systems,” Dokl. Ros. Akad. Nauk, Mat., 328, No. 2, 135–138 (1993).Google Scholar
- 13.Yu. M. Berezanskii, Expansion in Eigenfunctions of Self-Adjoint Operators [in Russian], Naukova Dumka Kiev (1965).Google Scholar
- 14.V. I. Polischyuk, and B.I. Ptashnyk, “Periodic solutions of a system of partial differential equations with constant coefficients,” Ukr. Mat. Zh., 32, No. 2, 239–243 (1980).Google Scholar
- 15.V. S. Il’kiv and B. I. Ptashnyk, “On a problem with nonlocal conditions for systems of partial differential equations with constant coefficients,” Different. Uravn., 20, No. 6, 1012–1023 (1984).Google Scholar
- 16.B. I. Ptashnyk, Ill-Posed Boundary-Value Problems for Partial Differential Equations [in Russian], Naukova Dumka, Kiev (1984).Google Scholar
- 17.N. M. Zadorozhna, Problems with Nonlocal Boundary-Value Conditions for Parabolic Equations and Systems [in Ukrainian], Author’s Abstract of the Candidate-Degree Thesis (Physics and Mathematics), L’viv (1995).Google Scholar
- 18.V. S. Il’kiv and B. I. Ptashnyk, “Representations and investigation of solutions of a nonlocal boundary-value problem for a system of partial differential equations,” Ukr. Mat. Zh., 48, No. 2, 184–194 (1996).Google Scholar
- 19.M. I. Matviichuk, “On one nonlocal parabolic boundary-value problem,” Ukr. Mat. Zh., 48, No. 3, 362–367 (1996).Google Scholar
- 20.V. P. Mikhailov, Partial Differential Equations [in Russian], Nauka, Moscow (1983).Google Scholar
- 22.M. A. Naimark, Linear Differential Operators [in Russian], Nauka, Moscow (1969).Google Scholar