In this paper, we study the regular solvability (in Sobolev spaces) of transmission problems for parabolic second-order systems with conjugation conditions of non-ideal contact type. The solution of such a problem has all generalized derivatives entering in the equation that are summable with some power \(p\in (1,\infty)\). One can express limit values of conormal derivatives at the interface in terms of combinations of limit values of the solution. This problem, arising when describing heat and mass transfer processes, differs from the classical statement of diffraction problems. The proof relies on derived a priori estimates and on the method of continuation in a parameter.

中文翻译：

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非理想接触条件下共轭问题的可解性

在本文中，我们研究了具有非理想接触型共轭条件的抛物型二阶系统传递问题的正规可解性（在Sobolev空间中）。这个问题的解决方案是将所有广义导数输入到方程中，这些导数可以用一些幂\（p \ in（1，\ infty）\）求和。一个人可以根据解的极限值的组合在界面上表示正态导数的极限值。在描述传热和传质过程时出现的这个问题不同于经典的衍射问题。证明依赖于推导的先验估计和参数连续的方法。