TITLE

Nonlinear Goursat-Darboux control problem: Conditions for the preservation of global solvability

AUTHOR(S)
Lisachenko, I. V.; Sumin, V. I.
PUB. DATE
June 2011
SOURCE
Differential Equations;Jun2011, Vol. 47 Issue 6, p863
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We consider the nonlinear vector Goursat-Darboux problem of general form with a control on the right-hand side in the differential equation. We consider the case in which its solution necessarily belongs to the class of functions with p-integrable (for some p > 1) mixed and first partial derivatives. In this connection, we use the fact that the first derivatives of such a solution are elements of spaces with a mixed norm; these spaces are much narrower than L. Sufficient conditions for the preservation of the global solvability of the problem under control perturbations are proved.
ACCESSION #
62806387

 

Related Articles

  • ON GOURSAT-DARBOUX BOUNDARY-VALUE PROBLEM FOR SYSTEMS OF NON-LINEAR DIFFERENTIAL EQUATIONS OF HYPERBOLIC TYPE. MARYNETS, V. V.; MARYNETS, K. V. // Miskolc Mathematical Notes;2013, Vol. 14 Issue 3, p1009 

    We construct the modification of the two-sided method with improved characteristics of convergence for approximate integration of boundary-value problem for systems of secondorder non-linear differential equations of the hyperbolic type on the plane when the bound of the domain of the...

  • On shape sensitivity analysis of the cost functional without shape sensitivity of the state variable. Kasumba, Henry; Kunisch, Karl // Control & Cybernetics; 

    general framework for calculating shape derivatives for domain optimization problems with partial differential equations as constraints is presented. The first order approximation of the cost with respect to the geometry perturbation is arranged in an efficient manner that allows the computation...

  • Multiplicity of Homoclinic Solutions for a Class of Nonperiodic Fourth-Order Differential Equations with General Perturbation. Liu Yang // Abstract & Applied Analysis;2014, p1 

    In this paper, we investigate a class of nonperiodic fourth-order differential equations with general perturbation. By using the mountain pass theorem and the Ekeland variational principle, we obtain that such equations possess two homoclinic solutions. Recent results in the literature are...

  • Darboux and binary Darboux transformations for the nonautonomous discrete KP equation. Willox, R.; Tokihiro, T.; Satsuma, J. // Journal of Mathematical Physics;Dec97, Vol. 38 Issue 12, p6455 

    Studies Darboux and binary Darboux transformations for a nonautononous discrete KP equation obtained from fermion analysis. Generalized Miwa transformations considered to obtain the equation; Linkage to discrete KP equation by gauge transformation; Use of the transformations to discuss general...

  • Robust H∞ Filter Design for Uncertain Fuzzy Descriptor Systems: LMI-Based Design. Assawinchaichote, Wudhichai; Sing Kiong Nguang // Proceedings of World Academy of Science: Engineering & Technolog;2007, Vol. 22, p523 

    This paper examines the problem of designing a robust H∞ filter for a class of uncertain fuzzy descriptor systems described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain nonlinear descriptor systems...

  • Stability against small noises in control problems with non-Lipschitz right-hand side of the dynamic equation. Khlopin, D. // Automation & Remote Control;Mar2008, Vol. 69 Issue 3, p419 

    Control problems in systems with non-Lipschitz right-hand side are studied for the performance functional continuously dependent on the path. Are considered two variants of the optimization problem depending on the fact whether the ally controls the realized path from the set generated by a...

  • Branch-and-bound algorithms for the partial inverse mixed integer linear programming problem. Wang, Lizhi // Journal of Global Optimization;Mar2013, Vol. 55 Issue 3, p491 

    This paper presents branch-and-bound algorithms for the partial inverse mixed integer linear programming (PInvMILP) problem, which is to find a minimal perturbation to the objective function of a mixed integer linear program (MILP), measured by some norm, such that there exists an optimal...

  • VARIATIONAL APPROACH TO SHAPE DERIVATIVES. Ito, Kazufumi; Kunisch, Karl; Peichl, Gunther H. // ESAIM: Control, Optimisation & Calculus of Variations;Jul2008, Vol. 14 Issue 3, p517 

    A general framework for calculating shape derivatives for optimization problems with partial differential equations as constraints is presented. The proposed technique allows to obtain the shape derivative of the cost without the necessity to involve the shape derivative of the state variable....

  • Robust solutions of quadratic optimization over single quadratic constraint under interval uncertainty. Jeyakumar, V.; Li, G. // Journal of Global Optimization;Feb2013, Vol. 55 Issue 2, p209 

    In this paper we examine non-convex quadratic optimization problems over a quadratic constraint under unknown but bounded interval perturbation of problem data in the constraint and develop criteria for characterizing robust (i.e. uncertainty-immunized) global solutions of classes of non-convex...

Share

Read the Article

Courtesy of NEW JERSEY STATE LIBRARY

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics