Some Doubly Nonlinear Evolution Equations in Banach Spaces

机译：Banach空间中的一些双重非线性发展方程

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The initial value problem is studied for the abstract evolution equation A(du/dt)+ B(u) contains f as a member, where A and B are maximal monotone operators from a Banach space W to its dual space W*, with A bounded and B 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 when A or B is linear and symmetric and one of them is strictly monotone. Applications are indicated for classes of nonlinear partial differential equations and systems.

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作者
Colli, P.;
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年度 1991
页码 p.1-33
总页数 33
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Nonlinear evolution equations; Boundary value problems; Cauchy problem; Nonlineardifferential equations; Partial differential equations; Existence theorems; Banach space; Approximation;

机译：非线性演化方程;边值问题; Cauchy问题;非线性微分方程;偏微分方程;存在定理; Banach空间;逼近;

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1. Doubly nonlinear evolution equations with non-monotone perturbations in reflexive banach spaces [J] . Akagi G. Journal of evolution equations . 2011,第1期

机译：自反banach空间中具有非单调摄动的双重非线性发展方程。
2. Doubly nonlinear evolution equations with non-monotone perturbations in reflexive Banach spaces [J] . Goro Akagi Journal of Evolution Equations . 2011,第1期

机译：自反Banach空间中具有非单调摄动的双非线性发展方程
3. Doubly nonlinear evolution equations governed by time-dependent subdifferentials in reflexive Banach spaces [J] . Akagi G Journal of Differential Equations . 2006,第1期

机译：自反Banach空间中依赖于时间的次微分控制的双非线性发展方程
4. EXISTENCE OF SLIDING MOTIONS FOR NONLINEAR EVOLUTION EQUATIONS IN BANACH SPACES [C] . Laura Levaggi AIMS International Conference on Dynamical Systems, Differential Equations and Applications . 2013

机译：Banach空间中非线性演化方程的滑动运动的存在性
5. Nonlinear evolution equations and optimization problems in Banach spaces. [D] . Lee, Haewon. 2005

机译：Banach空间中的非线性发展方程和优化问题。
6. ON A „MONOTONICITY METHOD FOR THE SOLUTION OF NONLINEAR EQUATIONS IN BANACH SPACES [O] . George J. Minty 1963

机译：Banach空间中非线性方程解的单调性方法
7. Doubly nonlinear evolution equations with non-monotone perturbations in reflexive Banach spaces [O] . Akagi Goro 2011

机译：自反Banach空间中具有非单调摄动的双非线性发展方程
8. Nonlinear Evolution Equations in Banach Spaces. [R] . Evans, L. C. 1975

机译：Banach空间中的非线性发展方程。

Some Doubly Nonlinear Evolution Equations in Banach Spaces

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