Vladimir Vladimirovich Goncharov

goncha@uevora.pt

Assistant Professor

Ph.D. Thesis:   Viable Solutions to Differential Inclusions with Nonconvex Right-Hand Side
                           Irkutsk Computing Center,  RAS,  Rússia,  1992

Research Interests:  Non-smooth Analysis

Scientific Projects:

• June - December 1994, CIMA-UE, Évora (Portugal), NATO Cooperation Partners research grant (CP R1/B/94/PO).

• November 1995 Research Project "Optimal Control and Differential Games: Theory, Numerical Methods and Applications", INTAS grant (INTAS-93-2622).

• 1993 - 1995 Research Project "Continuous Selections of Multivalued Mappings in Functional Spaces and their Applications" supported by the Russian Foundation of Basic Research (grant N 93-011-264).

• 1996 - 1998 Research Project "Nonconvex Problems in Differential Inclusions, Calculus of Variations and Optimal Control" supported by the Russian Foundation of Basic Research (grant N 96.01.00326).

• 1999 - 2001 Research Project "The Properties of Dynamical Systems Concerned with the Structure of their Solution Sets and Applications" supported by the Russian Foundation of Basic Research (grant N 99.01. 00216).

•  1999 - 2001 Research Project "Nonconvex Variational Problems", supported by FCT (Portugal) (POCTI/36422/MAT/1999).

• 2003 - 2006 Research Project "Optimization and Calculus of Variations" supported by FCT (Portugal) (787/2003-2005).

• Janeiro 2005 - present time Research Project "Differential Inclusions and Variational Problems" supported by FCT (Portugal) (POCTI/MAT/55524/2004 - Matemática

Publications:

• Goncharov V.V. Some Properties of Solutions to Differential Inclusions with Noncompact-valued Right-Hand Side in a Banach Space// In the book "Lyapunov´s Functions and their Applications", Nauka, Sib. otd., Novosibirsk, 1987, 214-230.

• Goncharov V.V. On Existence of Solutions of some Type Differential Inclusions on a Compact Set// Sib. Math. J., V.31-2 (1991), 727-732.

• Tolstonogov A.A., Goncharov V.V. On Continuous Selections and Properties of Solutions of Differential Inclusions with m-accretive Operators// Soviet Math. Dokl., V.42, N 3 (1991), 861-865.

• Goncharov V.V. Existence Theorems for Solutions of Differential Inclusions with a Lower Semicontinuous Right-Hand Side on a Locally Compact Set// Differ. Uravnenija, V.27, N 12 (1992), 1446-1452.

• Tolstonogov A.A., Goncharov V.V. Joint Continuous Selections of Multivalued Mappings with Nonconvex Values, and their Applications// Math. USSR Sbornik, V.73, N 2 (1992), 319-339.

• Tolstonogov A.A., Goncharov V.V. On Sublinear Functionals Defined in the Space of Bochner Integrable Functions// Sib. Math. J., V.35-1 (1994), 178-188.

• Goncharov V.V., Tolstonogov A.A. Continuous Selections of the Family of Nonconvex-valued Mappings with a Noncompact Domain// Sib. Math. J., V.35-1 (1994), 479-494.

• Goncharov V.V. Some Properties of Viability Problems Depending on a Parameter// NoDEA, N 2 (1995), 1-19.

• Colombo G., Goncharov V.V. Existence of a Nonconvex Optimal Control Problem with a Nonlinear Dynamics// Nonlin. Anal., Theory, Meth. and Appl., V.24, N 6 (1995), 795-800.

• Colombo G., Goncharov V.V., Ramazzina E. On a Class of Nonconvex and Nonlinear Optimal Control Problems// NoDEA, N 3 (1996), 115-126.

• Goncharov V.V., Ornelas A. On Minima of a Functional of the Gradient: a Continuous Selection// Nonlin. Anal., Theory, Meth. and Appl., V.27, N 10 (1996), 1137-1146.

• Goncharov V.V. Co-density and other Properties of the Solution Set of Differential Inclusions with Noncompact Right-Hand Side// Discuss. Math., Dif. Inclusions, V.16 (1996), 103-120.

• Dal Maso G., Goncharov V.V., Ornelas A. A Lipschitz Selection from the Set of Minimizers of a Nonconvex Functional of the Gradient// Nonlin. Anal., Theory, Meth. and Appl., V.37 (1999), 707-717.

• Goncharov V.V., Timoshin S.A. On a Class of Evolution Equations: Existence of Solutions with the Functional Boundary Conditions// Matem. Zametki, V.65, N 1 (1999), 48-60.

• Colombo G., Goncharov V.V. The Sweeping Processes without Convexity// Set-Valued Analysis, N 7 (1999), 357-374.

• Colombo G., Goncharov V.V. A Class of Non-convex Sets with Locally Well-posed Projection// Preprint SISSA, Ref. S.I.S.S.A. 78/99/M (July 1999).

• Colombo G., Goncharov V.V. The Sweeping Processes without Convexity// Proc. of Int. Conf. on Dif. Equat., Berlin, Germany, August 1999, ed. B.Fiedler, K.Groger, J.Spekels, 2000, 494-496.

• Goncharov V.V., Goncharova E.V. Functional Boundary Value Problems for a Class of Evolution Inclusions with an Unbounded Linear Operator// Differ. Uravnenija, V. 37, N 2 (2001), 195-204.

• Colombo G., Goncharov V.V. Variational Inequalities and Regularity Properties of Closed Sets in Hilbert Spaces// J. Convex Anal., V.8 (2001), 197-221.

• Colombo G., Goncharov V.V. Continuous Selections via Geodesics// Topol. Meth. in Nonlin. Anal., V.18 (2001), 171-182.

• V.V.Goncharov, A.Ornelas. On Minima of a Functional of the Gradient: Upper and Lower Solutions// Nonlin. Anal., Theory, Meth. and Appl., V.64 (2006), 1437-1459.

• V.V. Goncharov. Minimizers of a Functional of the Gradient which are Stable with respect to Affine Boundary Data// Sib. Adv. in Math., V.16, N 3 (2006), 1-13.

• V.V.Goncharov, A.Ornelas. Surfaces Changing Continuously with Affine Boundary Data and Having Gradients on a Prescribed Set// Proc. of Int. Conf. on Dif. Equat., Lisbon, Portugal, July 1995, ed. L.Magalhães, C.Rocha, L.Sanchez, 1998, 386-391.

• Tolstonogov A.A., Goncharov V.V. On Solutions of Differential Inclusion with Noncompact-valued Right-Hand Side in a Banach Space// Manuscript is deposited in Russian Research Institute of Technical Information, Moscow, 1986.