Papers
On the large time behavior of the solutions of a nonlocal ordinary differential equation with mass conservation
- AuthorDanielle Hilhorst (Hiroshi Matano, Thanh Nam Nguyen, Hendrik Weber)
- JournalJournal of Dynamics and Differential Equations 28 (2016
- Link https://doi.org/10.1007/s10884-015-9465-7
- Classification of papersSCI
We consider an initial value problem for a nonlocal differential equation with a bistable nonlinearity in several space dimensions. The equation is an ordinary differential equation with respect to the time variable t, while the nonlocal term is expressed in terms of spatial integration. We discuss the large time behavior of solutions and prove, among other things, the convergence to steady-states. The proof that the solution orbits are relatively compact is based upon the rearrangement theory.
We consider an initial value problem for a nonlocal differential equation with a bistable nonlinearity in several space dimensions. The equation is an ordinary differential equation with respect to the time variable t, while the nonlocal term is expressed in terms of spatial integration. We discuss the large time behavior of solutions and prove, among other things, the convergence to steady-states. The proof that the solution orbits are relatively compact is based upon the rearrangement theory.