Preservation of the global solvability of a first-kind operator equation with controlled additional nonlinearity

A. V. Chernov

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 3, Tome 192 (2021), pp. 131-141.

Résumé

For the Cauchy problem associated with a first-kind evolutionary operator equation in a Banach space supplemented by a controlled term that depends nonlinearly on the phase variable, we obtain conditions for the preservation of unique global solvability under small variations of control (in other words, conditions for the stability of the existence of global solutions) and also a uniform estimate of the increment of solutions with respect to the norm of the space. As an example, we consider the initial-boundary-value problem for the Oskolkov system.

Détail

Mots-clés : evolution equation
Keywords: operator equation, Banach space, controlled nonlinearity, preservation of unique global solvability, stability of the existence of global solutions, Oskolkov's system of equations.

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