非线性抛物型微分包含积分解的生存性及正则性

Existence and regularity of integral solutions for nonlinear parabolic differential inclusions

研究Banach空间中受极小映射扰动的非线性抛物型微分包含积分解的生存性及正则性.利用非线性半群及极小映射的性质和不动点定理,证明其积分解的生存性,获其积分解之间按Housdorff距离的连续性.借助Lip-schitz条件、绝对连续函数的性质及Banach空间的自反严格凸性,获其积分解的唯一性且是强解.所获结果对受此类微分包含约束的分布参数最优控制问题的探讨奠定理论基础,同时有助于研究相关的非线性微分包含。

Existence and regularity of integral solutions are studied for nonlinear parabolic differential inclusions involving a m-dissipative operator and minimal mappings in Banach spaces. The existence is proved through nonlinear semigroup, properties of minimal mappings and fixed-point theorems, while continuity of the solutions is examined in the sense of Housdorff distance. On the other hand, uniqueness of integral solution and its regularity are obtained by means of Lipachitz conditions, properties of absolute continuous mappings, reflexivity and strict convexity of Banach spaces. All results acquired not only help solve distribution parameter optimal control problems subject to the differential inclnsions, but also study the problems of other differential inclusions.