In this paper, we establish space like strong unique continuation property for uniformly parabolic sublinear equations under appropriate structural assumptions. Our main result Theorem 1.1 constitutes the parabolic counterpart of the strong unique continuation result recently established in (Ruland, J. Differential Equations 265 (2018) 6009–6035) for elliptic sublinear equations with analogous structure conditions. Similar to that in (Ruland, J. Differential Equations 265 (2018) 6009–6035), this is accomplished via a new $L^2-L^2$ type Carleman estimate for a class of sublinear parabolic operators.

中文翻译：

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次线性抛物方程的像强唯一连续这样的空间

在本文中，我们在适当的结构假设下，为均匀抛物线亚线性方程建立了像强唯一连续性这样的空间。我们的主要结果定理1.1构成了最近在（Ruland，J.differential Equations 265（2018）6009-6035）中建立的具有类似结构条件的椭圆形次线性方程组的强唯一连续结果的抛物线形式。与（Ruland，J.Differential Equations 265（2018）6009-6035）中的类似，这是通过新的${\mathrm{大号}}^2-{\mathrm{大号}}^2$ 一类亚线性抛物线算子的Carleman估计类型。