About the Solution of One Bondary Value Problems

In this article, the conditions for the regular solution of the boundary problem for a class of second-order operator-differential equations with truncated coefficients are derived. These equations have been specifically constructed to mathematically determine the corrosion time of metals in aggressive environments, which has crucial implications in fields such as materials science and engineering. The study focuses on identifying the precise conditions under which the problem exhibits regular solvability, a key aspect of ensuring the reliability of the solutions in practical applications. Furthermore, the obtained conditions are explicitly expressed in terms of the operator coefficients of the equation, offering a more robust framework for understanding the solvability of such operator-differential equations in various contexts. These results contribute significantly to both the theoretical and applied aspects of mathematical physics and engineering, especially in the analysis of physical systems subject to corrosion and other environmental factors.