On the large time behavior of the solutions of a nonlocal ordinary differential equation with mass conservation
On the large time behavior of the solutions of a nonlocal ordinary differential equation with mass conservation
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具有质量守恒的非局部常微分方程解的大时间行为
DOI：
10.1007/s10884-015-9465-7
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
T.N. Nguyen and H. Weber
中科院分区：
文献类型：
--
作者：
D. Hilhorst;H. Matano;T.N. Nguyen and H. Weber
考虑了多维空间中一类具非线性项的非局部微分方程的初值问题。该方程是关于时间变量的常微分方程，而非局部项则用空间积分表示。我们讨论了大的时间行为的解决方案和证明，除其他事项外，收敛到稳态。解轨道是相对紧的证明是基于重排理论。
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 variablet, 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.