ON AN INITIAL BOUNDARY-VALUE PROBLEM FOR 1D HYPERBOLIC EQUATION WITH INTERIOR DEGENERACY: SERIES SOLUTIONS WITH THE CONTINUOUSLY DIFFERENTIABLE FLUXES
Анотація

Ключові слова
Повний текст:
PDF (English)Посилання
S. Abbott, Understanding Analysis, Springer, NY, 2015.
F. Alabau-Boussouira, P. Cannarsa, G. Leugering, Control and stabilization of degenerate wave equations, SIAM J. Control Optim., 55(3) (2017), 2052–2087.
J. Bai, S. Chai, Exact controllability for some degenerate wave equations, Mathematical Methods in the Applied Sciences, 55(3) (2020), 1–10, http://doi.org/ 10.1002/mma.6464.
V. L. Borsch, On initial boundary value problems for the degenerate 1D wave equation, Journal of Optimization, Differential Equations, and their Applications (JODEA), 27(2) (2019), 27–44.
S. ˇ Cani´c, E.H. Kim, A class of quasilinear degenerate elliptic problems, Journal of Differential Equations, 189 (2003), 71–98.
M. Colombo, A. Figalli, Regularity results for very degenerate elliptic equations, J. Math. Pures Appl., 101 (2014), 94–117.
A. R. Forsyth, Theory of Differential Equations, Part III Ordinary Differential Equations, Vol. IV, University Press, Cambridge, 1902.
H. Gajewski, K. Groger, K. Zacharias, Nichtlineare Operatorgleichungen und Operator Differentialgleichungen, Akad Verlag, Berlin, 1974.
F. Gray, G. B. Mathews, A Treatise on Bessel Functions and their Applications to Physics, MacMillan & Co, London, 1895.
A. Greenleaf, Y. Kurylev, M. Lassas, G. Uhlmann, Cloaking devices, electromagnetic wormholes, and transformation optics, SIAM Rev., 51 (2009), 3–33.
M. Gueye, Exact boundary controllability of 1-D parabolic and hyperbolic degenerate equations, SIAM J. Control Optim., 52 (2014), 2037–2054.
E. L. Ince, Ordinary Differential Equations, Longman, London, 1927.
P. I. Kogut, O. P. Kupenko, G. Leugering, Y. Wang, A note on weighted Sobolev spaces related to weakly and strongly degenerate differential operators, Journal of Optimization, Differential Equations, and their Applications (JODEA), 27(2) (2019), 1–22.
P. I. Kogut, O. P. Kupenko, G. Leugering, On boundary exact controllability of weakly and strongly degenerate wave equations, to appear, (2020).
G. Lumer, R. S. Phillips, Dissipative operators in a Banach space, Pacific Journal of Mathematics, 11(2) (1961), 679–698.
G. Marinoschi, R. M. Mininni, S. Romanelli, An optimal control problem in coefficients for a strongly degenerate parabolic equation with interior degeneracy, J. Optim. Theory Appl., 173 (2017), 56–77.
V. A. Rukavishnikov, E. I. Rukavishnikova, Dirichlet problem with degeneration of the input data on the boundary of the domain, Differential Equations, 52(5) (2016), 681–685.
F. Santambrogio, V. Vespri, Continuity in two dimensions for a very degenerate elliptic equation, Nonlinear Anal., 73 (2010), 3832–3841.
G. N. Watson, A Treatise on the Theory of Bessel Functions, University Press, Cambridge, 1922.
E. T. Whittaker, G. N.Watson, ACourse of Modern Analysis, University Press, Cambridge, 1927.
DOI: http://dx.doi.org/10.15421/142OO1
Посилання
- Поки немає зовнішніх посилань.
Індексування журналу
Журнал розміщено у наукометричних базах, репозитаріях та пошукових системах:
Адреса редколегії: 49050, Україна, Дніпровський національний університет імені Олеся Гончара, вул. Козакова 18, корп. 14, механіко-математичний факультет, д-р фіз.-мат. наук, проф. Когут П.І.
email: p.kogut@i.ua
Це видання має доступ за ліцензією Creative Commons «Attribution» («Атрибуция») 4.0 Всемирная.