On some doubly nonlinear evolution equations in Banach spaces
On some doubly nonlinear evolution equations in Banach spaces
复制标题
Banach空间中的一些双非线性演化方程
DOI：
10.1007/bf03167565
复制
发表时间：
1992
影响因子：
0.9
通讯作者：
P. Colli
中科院分区：
文献类型：
--
作者：
P. Colli
研究抽象发展方程A(Du/dt)+B(U)∋f的初值问题，其中a和B是从Banach空间W到其对偶空间W*的极大单调算子，其中A有界，B无界.在适当的强迫性条件下，当至少有一个算子是真凸下半连续函数的次微分时，证明了解的存在性。通过引入问题的适当时间离散化，然后通过单调性和紧性传递到极限，证明了存在定理。证明了当球面是线性对称的且其中一个是严格单调的时，唯一性得到了证明。给出了一类非线性偏微分方程组和系统的应用。
The initial value problem is studied for the abstract evolution equationA(du/dt)+B(u) ∋f, whereA andB are maximal monotone operators from a Banach spaceW to its dual spaceW*, withA bounded andB unbounded. Assuming suitable coerciveness conditions, the existence of a solution is established when at least one of the operators is the subdifferential of a proper convex lower semicontinuous function. The existence theorems are shown by introducing a suitable time discretization of the problem and then passing to the limit by monotonicity and compactness. Uniqueness is proved whenA orB is linear and symmetric and one of them is strictly monotone. Applications are indicated for classes of nonlinear partial differential equations and systems.