Irsiy elastiklik nazariyasining dinamik tenglamalar uchun teskari masalalarining global yechilishi
Ushbu dissertatsiya ishida irsiy elastiklik nazariyasining dinamik tenglamalari uchun teskari masalalarning global yechilishi tadqiq etilgan. Tadqiqotda vertikal bir jinsli bo'lmagan muhitlarda qovishqoq-elastiklik va termoelastiklik-qovishqoqlik tenglamalari uchun skalyar va matritsali yadrolarni aniqlash usullari ishlab chiqilgan, global yagona yechiluvchanlik va turg'unlik shartlari olingan. Shuningdek, ko'p o'lchovli teskari masalalarni o'rganishga yordam beradigan nazariy asoslar ishlab chiqilgan va ushbu masalalarning yechimlarini topish usullari ishlab chiqilgan.
Asosiy mavzular
- Inversion problems for hereditary elasticity theory: The dissertation investigates inverse problems for dynamic equations of memory type of elasticity theory. Methods for determining scalar and matrix kernels for viscoelastic and thermoviscoelastic equations in vertically inhomogeneous media have been developed, global unique solvability and stability conditions have been obtained. The theoretical foundations for studying multidimensional inverse problems and methods for finding their solutions have also been developed.
- Global solvability of inverse problems: The study focuses on the global solvability of inverse problems for dynamic equations of memory type in elasticity theory. It explores methods for determining kernels in viscoelastic and thermoviscoelastic equations, providing theoretical groundwork for solving multidimensional inverse problems.
- Viscoelasticity and thermoviscoelasticity: The research addresses problems related to viscoelasticity and thermoviscoelasticity, specifically focusing on inverse problems for dynamic equations. It develops methods for analyzing the behavior of materials with memory under various conditions.