tailieunhanh - Summary of doctoral thesis in mathematics: Stability and stabilization for some evolution equations in fluid mechanics

Purpose of thesis: Resear h thesis on the problem: The stability and stabilization of some evolution equations appear in fluid mechanics. | Summary of doctoral thesis in mathematics: Stability and stabilization for some evolution equations in fluid mechanics MINISTRY OF EDUCATION AND TRAINING HA NOI PEDAGOGICAL UNIVERSITY 2 NGUYEN VIET TUAN STABILITY AND STABILIZATION FOR SOME EVOLUTION EQUATIONS IN FLUID MECHANICS Spe iality: Mathemati al analysis Code: 9 46 01 02 SUMMARY OF DOCTORAL THESIS IN MATHEMATICS Ha Noi - 2019 This thesis has been ompleted at the Ha Noi Pedagogi al Uni- versity 2 S ientifi Advisor: Asso .Prof. PhD. Cung The Anh Referee 1: Referee 2: Referee 3: The thesis shall be defended at the University level Thesis Assessment Coun il at Ha Noi Pedagogi al University 2 on. The thesis an be found in the National Library and the Library of Ha Noi Pedagogi al University 2. INTRODUCTION 1. MOTIVATION AND HISTORY OF THE PROBLEM Partial differential evolution equations appear frequently in the of physi al and biologi al pro esses, su h as heat transfer and diffusion, pro ess of wave transmission in fluid me hani s and pop- ulation models in biology. The study of this equations lass has important meaning in s ien e and te hnology. That is why it has attra ted widespread attention. After studying the well-posedness of the problem, it is im- portant to study the long-time behavior of solutions, as it allows us to understand and predi t the future dynami s, sin e we an make the appropriate adjustments to a hieve the desired results. An effe tive approa h is the study of the existen e and stability of the stationary solutions. In mathemati al, the stationary solu- tions response orresponds to the stationary state of the pro ess, and is the solution of the orresponding ellipti problem. When the stationary solutions of the pro esses is not stability, people try to stabilize it by using appropriate ontrols, or using appropriate random noise. In re ent years, stability and