Project's information
Project's title | On the existence and the asymptotic behavior of solutions to fractional diffusion equations |
Project’s code | ĐLTE00.01-20/21 |
Research hosting institution | Institute of Mathematics |
Project leader’s name | Dr. Hoàng Thế Tuấn |
Project duration | 01/01/2020 - 31/12/2021 |
Project’s budget | 500 million VND |
Classify | Excellent |
Goal and objectives of the project | As we known, the classical heat transfer equation ∂u/∂t=∆u describes heat transfer in a homogeneous medium. Meanwhile, the time-fractional diffusion equation ∂_t^α u=∆u where α ϵ (0,1) and ∂_t^α is the fractional derivative in the Caputo sense, can be used to represent the singular diffusion (small diffusion pattern) caused by particle adhesion and trapping. Probabilistically, this equation concerns non-Markov memory processes. Our aim is to study the properties of solutions of time-fractional diffusion equations such as existence, uniqueness of solutions, numerical simulations and study of asymptotic properties of solutions. |
Main results | - Showed the asymptotic behaviour of solutions to time-fractional elliptic equations driven by a multiplicative white noise in the mean square sense. The second result above is a main content in the published paper: |
Novelty and actuality and scientific meaningfulness of the results | - By combining the eigenfunction expansion method for symmetry elliptic operators, the variation of constant formula for strong solutions to scalar stochastic fractional differential equations, Ito's formula and establishing a new weighted norm associated with a Lyapunov-Perron operator defined from this representation of solutions, we have shown the asymptotic behaviour of solutions to time-fractional elliptic equations driven by a multiplicative white noise in the mean square sense. As a consequence, we also prove existence, uniqueness and the convergence rate of solutions to their equilibrium point. |
Products of the project | Scientific papers in referred journals: 02 published papers are |