Uniqueness of solution of a heterogeneous evolution dam problem associated with a compressible fluid flow through a rectangular porous medium
This paper is concerned with an uniqueness of solution of the weak formulation of an evolution dam problem related to a compressible fluid flow through a two-dimensional, rectangular and heterogeneous porous medium. Note that our problem associated with the equation a(x_1)(u_{x_2}+\chi)_{x_2}-(u+\ch...
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| Main Author | |
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| Format | Journal Article |
| Language | English |
| Published |
20.11.2018
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| Subjects | |
| Online Access | Get full text |
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| Summary: | This paper is concerned with an uniqueness of solution of the weak
formulation of an evolution dam problem related to a compressible fluid flow
through a two-dimensional, rectangular and heterogeneous porous medium. Note
that our problem associated with the equation
a(x_1)(u_{x_2}+\chi)_{x_2}-(u+\chi)_t=0. Our technique is based on the idea
that we transform the weak form of this equation into a similar situation to
the proof of the uniqueness in the incompressible case (see [12]). It is also
difficult to adapt the proof obtained in [12] by using some properties of the
solutions as in [12, Sect. 2]. |
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| DOI: | 10.48550/arxiv.1811.08085 |