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Unique continuation and continuous dependence results for a severely ill-posed integrodifferential parabolic problem with a memory term in the principal part of the differential operator

机译:严重不适定的积分微分抛物问题的唯一连续和连续依赖性,其记忆项在微分算子的主要部分中

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摘要

We prove uniqueness and continuous dependence results for a severely ill-posed linear integrodifferential boundary-value parabolic problem with no initial condition. This latter condition is replaced with an additional boundary information prescribing the temperature on an open subset of the geometric domain ?. The integral operators entering the equation are defined by integrals of Volterra type with respect to time. In particular, the class of integrodifferential equations dealt with in this paper include those occurring in the linear theory of heat flow in a rigid body consisting of a material with thermal memory.
机译:我们证明了没有初始条件的严重不适定线性整数微分边值抛物问题的唯一性和连续依赖结果。后者的条件被附加的边界信息所代替,该边界信息规定了几何域α的开放子集上的温度。输入方程的积分算子由Volterra类型的时间积分定义。特别是,本文涉及的一类积分微分方程包括那些在具有热记忆材料的刚体中的热流线性理论中出现的方程。

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