Extended groups of semigroups and backward problems of heat equations

M. Arisawa

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arXiv · 1112.1746

Extended groups of semigroups and backward problems of heat equations

M. Arisawa

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Abstract

In this paper, we are concerned with backward solvabilities of heat equations, in an abstract framework. We show that semigroups $T_t$ in Banach spaces $X$, generated by heat operators, are extendable to groups in an extended space $E$, which is obtained by considering a sequence of wider Banach spaces containing $X$, i.e. $X$$/subset$$X_t$$/subset$$X_s$... $(t 0$. Another is the backward uniqueness of the semigroup $T_t$. For example, we prove the holomorphic semigroup satisfies the above conditions, and thus is extendable to a group in a larger functional space $E$. We also studied structual properties of the extended space $E$.

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M. Arisawa. 2011-12-08. Extended groups of semigroups and backward problems of heat equations. https://arxiv.org/abs/1112.1746

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