In this note we show that, under certain conditions on the coefficients, the solutions of the parabolic phase-lag heat conduction models are determined by an analytic semigroup for which the inner product determines the $H^2$-norm of the temperature. As a consequence the $H^2$-norm of the temperature decays in an exponential way.

中文翻译：

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抛物线相位滞后热传导理论重新审视

在本说明中，我们表明，在系数的某些条件下，抛物线相位滞后热传导模型的解由解析半群确定，其内积决定了 $H^2$- 温度标准。因此， $H^2$- 温度范数以指数方式衰减。