期刊
JOURNAL OF INVERSE AND ILL-POSED PROBLEMS
卷 23, 期 6, 页码 555-570出版社
WALTER DE GRUYTER GMBH
DOI: 10.1515/jiip-2014-0043
关键词
Boundary value problems for parabolic equations; ill-posed problems; integral representation's method
资金
- Russian Federation Government for scientific research under the supervision of leading scientist at the Siberian Federal University [14.Y26.31.0006]
- Russian Foundation for Basic Research [14-01-00544]
We consider a boundary value problem for a Lame type operator, which corresponds to a linearisation of the Navier-Stokes' equations for compressible flow of Newtonian fluids in the case where pressure is known. It consists of recovering a vector function, satisfying the parabolic Lame type system in a cylindrical domain, via its values and the values of the boundary stress tensor on a given part of the lateral surface of the cylinder. We prove that the problem is ill-posed in the natural spaces of smooth functions and in the corresponding Holder spaces; besides, additional initial data do not turn the problem to a well-posed one. Using the integral representation's method we obtain a uniqueness theorem and solvability conditions for the problem. We also describe conditions, providing dense solvability of the problem.
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