Local strong solutions in a quasilinear Moore-Gibson-Thompson type model for thermoviscoelastic evolution in a standard linear solid
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914304910950400 |
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| author | Claes, Leander Winkler, Michael |
| author_facet | Claes, Leander Winkler, Michael |
| contents | This manuscript is concerned with the evolution system \[
\left\{ \begin{array}{l}
u_{ttt} + αu_{tt} = \big(γ(Θ) u_{xt}\big)_x + \big( \widehatγ(Θ) u_x\big)_x,
Θ_t = D Θ_{xx} + Γ(Θ) u_{xt}^2,
\end{array} \right. \] which arises as a simplified model for heat generation during acoustic wave propagation in a one-dimensional viscoelastic medium of standard linear solid type.
Under the assumptions that $D>0$ and $α\ge 0$, and that $γ, \widehatγ$ and $Γ$ are sufficiently smooth with $γ>0, \widehatγ>0$ and $Γ\ge 0$ on $[0,\infty)$, for suitably regular initial data a statement on local existence and uniqueness of solutions in an associated Neumann problem is derived in a suitable framework of strong solvability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_04005 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Local strong solutions in a quasilinear Moore-Gibson-Thompson type model for thermoviscoelastic evolution in a standard linear solid Claes, Leander Winkler, Michael Analysis of PDEs 74H20, 74F05, 35L05 This manuscript is concerned with the evolution system \[ \left\{ \begin{array}{l} u_{ttt} + αu_{tt} = \big(γ(Θ) u_{xt}\big)_x + \big( \widehatγ(Θ) u_x\big)_x, Θ_t = D Θ_{xx} + Γ(Θ) u_{xt}^2, \end{array} \right. \] which arises as a simplified model for heat generation during acoustic wave propagation in a one-dimensional viscoelastic medium of standard linear solid type. Under the assumptions that $D>0$ and $α\ge 0$, and that $γ, \widehatγ$ and $Γ$ are sufficiently smooth with $γ>0, \widehatγ>0$ and $Γ\ge 0$ on $[0,\infty)$, for suitably regular initial data a statement on local existence and uniqueness of solutions in an associated Neumann problem is derived in a suitable framework of strong solvability. |
| title | Local strong solutions in a quasilinear Moore-Gibson-Thompson type model for thermoviscoelastic evolution in a standard linear solid |
| topic | Analysis of PDEs 74H20, 74F05, 35L05 |
| url | https://arxiv.org/abs/2602.04005 |