The principal eigenvalue of a space–time periodic parabolic operator
The principal eigenvalue of a space–time periodic parabolic operator
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DOI：
10.1007/s10231-008-0075-4
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发表时间：
2009-04
影响因子：
1
通讯作者：
Grégoire Nadin
中科院分区：
文献类型：
--
作者：
Grégoire Nadin
本文研究抛物型算子$${数学{L}\Phi=Partial_{t}\Phi-\nabla\Cot(A(t，x)\nabla\Phi)+Q(t，x)\CDot\nabla\Phi-\Mu(t，x)\Phi}$$的广义主本征值，其中系数为周期整数x。我们给出了这个特征值的定义，并证明了它可以用与有界域上的同一算子相关的一系列主特征值来逼近，并且在时间上是周期性的，在空间上是Dirichlet边界条件。接下来，我们定义了与算子相关的一族周期主本征值，并用它来刻画广义主本征值。最后，我们研究了所有这些本征值对系数的依赖性。
This paper deals with the generalized principal eigenvalue of the parabolic operator $${\mathcal{L}\phi = \partial_{t}\phi - \nabla \cdot(A(t, x)\nabla\phi) + q(t, x) \cdot \nabla\phi - \mu(t, x)\phi}$$ , where the coefficients are periodic intandx. We give the definition of this eigenvalue and we prove that it can be approximated by a sequence of principal eigenvalues associated to the same operator in a bounded domain, with periodicity in time and Dirichlet boundary conditions in space. Next, we define a family of periodic principal eigenvalues associated with the operator and use it to give a characterization of the generalized principal eigenvalue. Finally, we study the dependence of all these eigenvalues with respect to the coefficients.