Address: Markusa st. 22, Vladikavkaz,
362027, RNO-A, Russia
Phone: (8672)50-18-06
E-mail: rio@smath.ru
DOI: 10.23671/VNC.2014.3.10238
On total preservation of global solvability for a goursat problem associated with a controlled semilinear pseudoparabolic equation
Chernov A. V.
Vladikavkaz Mathematical Journal 2014. Vol. 16. Issue 3.
Abstract: We investigate a Goursat problem associated with a controlled fourth order semilinear equation of the pseudoparabolic type having various applications. Under some hypotheses we prove the total (with respect to the set of admissible controls) preservation of global solvability for the considered problem.
Keywords: Goursat problem, semilinear controlled pseudoparabolic equation, total preservation of global solvability, functional operator equation of the Hammerstein type
For citation: Chernov A. V. On total preservation of global solvability for a goursat problem associated with a controlled semilinear pseudoparabolic equation // Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 16, no. 3, pp.55-63. DOI 10.23671/VNC.2014.3.10238
1. Vajnberg M. M. Variacionnyj Metod i Metod Monotonnyh Operatorov
v Teorii Nelinejnyh Uravnenij, Moskva, Nauka, 1972, 416 p.
(Russian).
2. Mamedov I. G. A non-classical formula for integration by parts
related to goursat problem for a pseudoparabolic equation.
Vladikavk. Mat. Zhurn. [Vladikavk. Math. J.], 2011, vol. 13, no. 4,
pp. 40-51 (Russian).
3. Potapov D. K. Control problems for equations with a spectral
parameter and a discontinuous operator under perturbations. Zhurn.
Sib. Fed. Un-ta. Ser. Matematika i Fizika [J. Sib. Fed. Univ. Math.
Phys.], 2012, vol. 5, no. 2, pp. 239-245 (Russian).
4. Potapov D. K. Optimal control of higher order elliptic
distributed systems with a spectral parameter and discontinuous
nonlinearity. J. Comp. Systems Sci. International, 2013. vol. 52,
no. 2, pp. 180-185.
5. Sumin V. I., Chernov A. V. Operators in the spaces of measurable
functions: the Volterra property and quasinilpotency. Differential
Equations, 1998, vol. 34, no. 10, pp. 1403-1411.
6. Tribel' H. Teorija Interpoljacii, Funkcional'nye Prostranstva,
Differencial'nye Operatory, Moscow, Mir, 1980, 664 p. (Russian).
7. Chernov A. V. A majorant criterion for the total preservation of
global solvability of controlled functional operator equation.
Russian Mathematics, 2011, vol. 55, no. 3, pp. 85-95.
8. Chernov A. V. A majorant-minorant criterion for the total
preservation of global solvability of a functional operator
equation. Russian Mathematics, 2012, vol. 56, no. 3, pp. 55-65.
9. Chernov A.V. On a generalization of the method of monotone
operators. Differential Equations, 2013, vol. 49, no. 4, pp.
517-527.
