Controllability of pseudoparabolic integro-differential systems with memory
DOI:
https://doi.org/10.17721/1812-5409.2026/1.20Keywords:
pseudoparabolic integro-differential equation, Volterra operator, memory effect, a priori estimates, well-posedness, generalized solvabillity, controllability, optimal controlAbstract
The paper studies linear pseudoparabolic integro-differential equations with a Volterra-type integral term, which provide an effective mathematical framework for describing dynamic processes with memory and nonlocal interactions. Such mathematical models are characteristic of various areas of applied research, where the evolution of a system depends not only on current conditions but also on its previous state. Typical examples include the behavior of viscoelastic materials (such as polymers, biopolymers, and high-temperature metals), the processes of groundwater filtration and contaminant transport in porous media, as well as in problems related to the transport of heat and nutrients in tissues.
The aim of the study is to generalize known theoretical results to a broader class of pseudoparabolic equations by introducing additional terms into both the differential and integral parts of the operators. To achieve this goal, the methodology of a priori estimates in negative norms, developed by S. I. Lyashko and his colleagues, is employed. The proposed approach enables the investigation of well-posedness, generalized solvability, and issues of controllability and optimal control for systems with distributed parameters.
The main result of the study is the establishment of a priori estimates in negative norms that account for the new terms introduced into the pseudoparabolic integro-differential equation. A key distinction of this work from previous studies is that the obtained estimates are proven without imposing non-negativity assumptions on the lower-order terms of the differential operator. This substantially broadens the applicability of the theory, allowing the extension of theorems on the well-posedness of initial-boundary value problems, as well as results on controllability and the existence of optimal control, to a wider class of pseudoparabolic-type systems.
Pages of the article in the issue: 147 - 160
Language of the article: English
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