Extended groups of semigroups and backward problems of heat equations

Details Extended groups of semigroups and backward problems of heat equations Extended groups of semigroups and backward problems of heat equations

2011-12-08

arxiv.org/abs/1112.1746v1

Mathematics

Analysis of PDEs

Master's thesis

Scientific paper

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$... $(t0$. 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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