On total preservation of global solvability for a goursat problem associated with a controlled semilinear pseudoparabolic equation

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Home Editorial board Publication ethics Peer review guidelines Latest issue All issues Rules for authors Online submission system's guidelines Submit manuscript Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 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 Language: Russian Download the full text 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 + References 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. The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses. ← Contents of issue


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