The maximal regularity of the third-order differential equation and its applications
Ospanov K. Ospanov M.
April 2024John Wiley and Sons Ltd
Mathematical Methods in the Applied Sciences
2024#47Issue 64895 - 4910 pp.
In this work, we study the solvability and maximal regularity questions for the singular third-order differential equation with unbounded coefficients and some applications. Unlike previously studied cases, the leading and intermediate coefficients of this equation can grow independently. We obtain sufficient coefficient conditions for correctness of this equation and compactness for inverse of the corresponding differential operator. We also prove the maximal regularity estimate for a generalized solution. Using these results, we obtain upper and lower estimates for the number of Kolmogorov (Formula presented.) -diameters of the set associated with the linear Korteweg–de Vries equations solutions. We give an example and show that from the above inequalities follow two-sided estimates of the Kolmogorov (Formula presented.) -diameters.
coercive estimate , compactness , correctness , genegalized solution , Kolmogorov diameter , resolvent , singular differential equation
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Faculty of Mathematics and Mechanics, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan
Faculty of Mathematics and Mechanics
10 лет помогаем публиковать статьи Международный издатель
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