Oscillations in Compressible Navier-Stokes and Homogenization in Phase Transition problems
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913333732442112 |
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| author | Tzavaras, Athanasios E. |
| author_facet | Tzavaras, Athanasios E. |
| contents | In the first part of this article we present some exact solutions for special hyperbolic-parabolic systems with sustained oscillations induced by the initial data, most notably the compressible Navier-Stokes system with non-monotone pressure. This part complements \cite{Tzavaras23} where such examples are extensively studied. The second part deals with the problem of homogenization for one-dimensional models describing phase transitions for viscoelastic materials . Ideas from the kinetic formulation of conservation laws are employed to derive effective equations that describe the propagation of oscillations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_18455 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Oscillations in Compressible Navier-Stokes and Homogenization in Phase Transition problems Tzavaras, Athanasios E. Analysis of PDEs 35Q30 76N10 35L60 74H35 In the first part of this article we present some exact solutions for special hyperbolic-parabolic systems with sustained oscillations induced by the initial data, most notably the compressible Navier-Stokes system with non-monotone pressure. This part complements \cite{Tzavaras23} where such examples are extensively studied. The second part deals with the problem of homogenization for one-dimensional models describing phase transitions for viscoelastic materials . Ideas from the kinetic formulation of conservation laws are employed to derive effective equations that describe the propagation of oscillations. |
| title | Oscillations in Compressible Navier-Stokes and Homogenization in Phase Transition problems |
| topic | Analysis of PDEs 35Q30 76N10 35L60 74H35 |
| url | https://arxiv.org/abs/2404.18455 |