Initial boundary-value problem for parabolic systems in dihedral domains
UDC 517.9 We present some results on the smoothness of the solution of the initial boundary-value problem for the parabolic system of partial differential equations $$u_t -(-1)^m P(x,t,D_x )u = f(x,t)\quad \text{in } \Omega_T := \Omega\times(0,T),$$ $$\frac{\partial^j u}{\partial \nu^j } = 0 \quad \...
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| Date: | 2020 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2020
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1094 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.9
We present some results on the smoothness of the solution of the initial boundary-value problem for the parabolic system of partial differential equations $$u_t -(-1)^m P(x,t,D_x )u = f(x,t)\quad \text{in } \Omega_T := \Omega\times(0,T),$$ $$\frac{\partial^j u}{\partial \nu^j } = 0 \quad \text{on } (\partial\Omega \backslash M) \times (0, T)$$ $$u(x,0)=0, $$ in the domain $\Omega_T$ of dihedral type, where $P$ is an elliptic operator with variable coefficients. The dependence of the regularity of solutions on the distribution of eigenvalues for the corresponding spectral problems is shown. The obtained results are useful for understanding the asymptotics of the weak solution near the singular edge of dihedral domains. |
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| DOI: | 10.37863/umzh.v72i7.1094 |