Analytic resolvent semilinear integro‐differential systems: Existence and optimal control
Rohit Patel, Anurag Shukla, Shimpi Singh Jadon, Arun Kumar Singh
Abstract
The primary contributions of this article are the existence of mild solutions and optimal control for analytic resolvent semilinear integro‐differential systems. Using Lipschitz nonlinearity and the Banach fixed point theorem, we demonstrate results for mild solutions. Using the ‐semigroup, minimizing sequence, Gronwall's inequality, and fundamentals of functional operator theory, we obtain the results for optimal control.
Topics & Concepts
MathematicsResolventLipschitz continuitySemigroupFixed-point theoremBanach spaceAnalytic semigroupNonlinear systemResolvent formalismGronwall's inequalityOperator (biology)Fixed pointApplied mathematicsPure mathematicsMathematical analysisInequalityFinite-rank operatorPhysicsTranscription factorQuantum mechanicsGeneRepressorChemistryBiochemistryNonlinear Differential Equations AnalysisNumerical methods for differential equationsStability and Controllability of Differential Equations