5 papers · 1 filter
Uniqueness of the stochastic Keller-Segel model in one dimension
Erika Hausenblas, Debopriya Mukherjee, Thanh Tran
In a recent paper (J. Differential Equations, 310: 506-554, 2022), the authors proved the existence of martingale solutions to a stochastic version of the classical Patlak-Keller-S…
A parabolic equation on domains with random boundaries
Duong Thanh Pham, Thanh Tran
A heat equation with uncertain domains is thoroughly investigated. Statistical moments of the solution is approximated by the counterparts of the shape derivative. A rigorous proof…
The one-dimensional stochastic Keller--Segel model with time-homogeneous spatial Wiener processes
Erika Hausenblas, Debopriya Mukherjee, Thanh Tran
Chemotaxis is a fundamental mechanism of cells and organisms, which is responsible for attracting microbes to food, embryonic cells into developing tissues, or immune cells to infe…
Remarks on Sobolev norms of fractional orders
Thanh Tran
When a function belonging to a fractional-order Sobolev space is supported in a proper subset of the Lipschitz domain on which the Sobolev space is defined, how is its Sobolev norm…
Existence of arbitrarily smooth solutions of the LLG equation in 3D with natural boundary conditions
Michael Feischl, Thanh Tran
We prove that the Landau-Lifshitz-Gilbert equation in three space dimensions with homogeneous Neumann boundary conditions admits arbitrarily smooth solutions, given that the initia…