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首页> 外文会议>International Conference "Functional Analysis in Interdisciplinary Applications" >Solution of the Multidimensional Problem for the Parabolic Equation with Incompatible Initial and Boundary Data in the H?lder and Weighted Spaces
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Solution of the Multidimensional Problem for the Parabolic Equation with Incompatible Initial and Boundary Data in the H?lder and Weighted Spaces

机译：抛物线方程的多维问题解决了H·焊盘和加权空间中不相容的初始和边界数据的抛物线方程

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摘要

Studying the solutions of the boundary value problems for the parabolic equations in the Holder spaces we should require the fulfilment of the compatibility conditions of the initial and boundary data of all necessary orders, they provide the continuity of the solution and its derivatives of all acceptable orders up to the boundary and boundedness of the H?lder constants of the highest derivatives in the closure of a domain. Such problems describe the physical processes which go continuously all the time since the beginning of the processes. If we consider the processes (for instance, heating or cooling), which are not continuous at the initial moment, then compatibility conditions of the initial and boundary data of the problems modeling this processes can not be fulfilled, but processes go, that is the problems with incompatible initial and boundary data have physical sense and they can have the solutions. There is considered a multidimensional first boundary value problem for the parabolic equation with incompatible initial and boundary data of the zero and first orders. It is proved that the solution of the problem may be represented as a sum of a H?lder solution and two singular ones corresponding these two incompatible initial and boundary conditions. The singular solutions belong to the weighted space with parabolic weights and space of the functions, the highest derivatives of which are not continuous, but bounded. These regular and singular solutions are unique, the estimates for them are obtained.
机译：研究持有人空间中抛物线方程的边值问题的解析问题，我们应该要求满足所有必要订单的初始和边界数据的兼容性条件，它们提供了解决方案的连续性及其所有可接受订单的衍生物到域关闭中最高衍生物的H·彼此常数的边界和界限。此类问题描述了自进程开始以来一直连续地完成的物理过程。如果我们考虑在初始时刻不连续的过程（例如，加热或冷却），那么无法满足建模此过程的问题的初始和边界数据的兼容性条件，但流程GO，即初始和边界数据不兼容的问题具有物理意义，它们可以具有解决方案。抛物线方程认为具有零和第一订单的初始和边界数据的抛物线方程的多维第一边值问题。事实证明，问题的解决方案可以表示为H·粘度溶液和两个奇异的初始和边界条件的2个奇异溶液的总和。奇异解决方案属于具有抛物面重量和功能的空间的加权空间，其最高衍生物不是连续的，但有界。这些常规和奇异的解决方案是独一无二的，获得了它们的估计。

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