Mutational analysis with transitions whose domains vary in state and that are not necessarily Lipschitz continuous in time
Mutational analysis with transitions whose domains vary in state and that are not necessarily Lipschitz continuous in time
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DOI：
10.1016/j.jmaa.2021.124967
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发表时间：
2021-06
影响因子：
1.3
通讯作者：
Kazukiyo Takami;N. Tanaka
中科院分区：
文献类型：
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作者：
Kazukiyo Takami;N. Tanaka
Lorenz改进了Aubin在突变分析方面的一项开创性工作，即时间跃迁的全局Lipschitz连续性被削弱为局部Lipschitz连续性，状态的可缩性被一个额外的结构不等式所取代。这种不平等最近被小林和第二作者消除了。局部Lipschitz连续假设对一般Banach空间中的半线性方程和带时滞的突变方程的应用仍有一定的局限性，而以往的结果由于所用区域含有公共核的转移而不能直接应用于混合问题。为了克服这种情况，我们引入了一类新的跃迁，它们的定义域在状态上变化，并且不一定满足局部Lipschitz连续性，以及一族依赖于状态和时间的度量族的跃迁的新的结构条件。在这种结构条件和跃迁的增长条件下，主要定理断言，关于类度规泛函的所谓亚切条件和耗散性条件确保给定的突变方程是适定的。
A pioneering work of Aubin for mutational analysis was improved by Lorenz in that global Lipschitz continuity of transitions in time was weakened to local Lipschitz continuity and contractivity in state was replaced by an additional structural inequality. This inequality was recently eliminated by Kobayashi and the second author. Local Lipschitz continuity assumption is still restrictive in its application to semilinear equations in general Banach spaces and mutational equations with delay, and the previous results cannot be directly applied to mixed problems because they use transitions whose domains contain a common core. To overcome such situations, we introduce a new class of transitions whose domains vary in state and that do not necessarily satisfy local Lipschitz continuity, and a new structural condition for transitions by a family of metrics depending on state and time. Under this structural condition and a growth condition for transitions, the main theorem asserts that the so-called subtangential condition and a dissipativity condition with respect to a metric-like functional ensure that a given mutational equation is well-posed.