Inverse Spectral Problems and Mathematical Models of Continuum Mechanics
DOI:
https://doi.org/10.14529/mmp190201Ключевые слова:
обратная спектральная задача, дискретный оператор, оператор четвертого порядка, самосопряженный оператор, собственные числа, собственные функции, некорректно поставленные задачи.Аннотация
Статья носит обзорный характер и содержит результаты в области спектральных задач для математических моделей с дискретным полуограниченным оператором. В основу теории положены линейные формулы вычисления собственных чисел дискретного оператора и редукция рассматриваемых спектральных задач к интегральному уравнению Фредгольма первого рода. Разработанный на основе метода Галеркина вычислительно эффективный численный метод решения обратных спектральных задач для дискретных полуограниченных операторов позволяет с высокой точностью восстанавливать коэффициентные функции краевых задач. Полученные результаты применимы при исследовании задач для дифференциальных операторов любого порядка. Приведены результаты численного решения обратной спектральной задачи для возмущенного дифференциального оператора четвертого порядка. Проведено исследование некоторых математических моделей механики сплошной среды на основе спектральных задач для дискретного полуограниченного оператора.Библиографические ссылки
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