Abstract
AbstractIn this paper, we study the controllability of two problems involving the same Chandrasekhar-type integral equation, but under different kinds of controls. A viability condition is imposed as well. We provide existence results of continuous trajectories coupled to continuous controls. Then, in the non-viable case, we investigate the optimal estimates to be taken in view of the existence of solutions for both problems. The last part of the paper deals with the application of the previous results to the classical Chandrasekhar equation, first showing the existence of a viable continuous solution, then providing also uniqueness and approximability. Two examples of controllability problems governed by this equation are given.
Funder
Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni
FRB 2019 of the University of Perugia “Integrazione, approssimazione, analisi nonlineare e loro applicazioni”
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Geometry and Topology,Modeling and Simulation
Reference26 articles.
1. Appell, J.: Measures of noncompactness, condensing operators and fixed points: an application-oriented survey. Fix. Point Theo. 6(2), 157–229 (2005)
2. Argyros, I.K.: Quadratic equations and applications to Chandrasekhar’s and related equations. Bull. Austral. Math. Soc. 32(2), 275–292 (1985)
3. Argyros, I.K.: On a class of quadratic integral equations with perturbation. Funct. Approx. Comment. Math. 20, 51–63 (1992)
4. Banaś, J., Goebel, K.: Measures of noncompactness in Banach spaces. Lecture Notes in Pure and Applied Mathematics, vol. 60. Marcel Dekker Inc, New York (1980)
5. Banaś, J., Lecko, M., El-Sayed, W.G.: Existence theorems for some quadratic integral equations. J. Math. Anal. Appl. 222, 276–285 (1998)
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