论文标题
关于多谐热方程的库奇问题不足的问题
On the ill-posed Cauchy problem for the polyharmonic heat equation
论文作者
论文摘要
我们考虑了恢复功能的多态热方程的不足的库奇问题，满足了在半空间$ {\ mathbb r}^n \ geq 1 $ n $ n $ n $ n $ n $ geq的圆柱域中的等式$（\ partial _t +（ - eartial _t +（ - δ）^m）u = 0 $ = 0 $，拉普拉斯操作员通过其值及其正常衍生物的值在圆柱体侧面的给定部分上达到$（2M-1）$的订单。我们获得了有关该问题的唯一定理，并根据与Cauchy数据相关的抛物线电位的真实分析延续而获得了其解决性的标准。
We consider the ill-posed Cauchy problem for the polyharmonic heat equation on recovering a function, satisfying the equation $(\partial _t + (- Δ)^m) u=0$ in a cylindrical domain in the half-space ${\mathbb R}^n \times [0,+\infty)$, where $n\geq 1$, $m\geq 1$ and $Δ$ is the Laplace operator, via its values and the values of its normal derivatives up to order $(2m-1)$ on a given part of the lateral surface of the cylinder. We obtain a Uniqueness Theorem for the problem and a criterion of its solvability in terms of the real-analytic continuation of parabolic potentials, associated with the Cauchy data.
