TY - JOUR
AU - P. T. Duong
PY - 2020/07/15
Y2 - 2020/08/12
TI - Initial boundary-value problem for parabolic systems in dihedral domains
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 72
IS - 7
SE - Research articles
DO - 10.37863/umzh.v72i7.1094
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/1094
AB - UDC 517.9We present some results on the smoothness of the solution of the initial boundary-value problem for the parabolic system of partial differential equations $$u_t -(-1)^m P(x,t,D_x )u = f(x,t)\quad \text{in } \Omega_T := \Omega\times(0,T),$$ $$\frac{\partial^j u}{\partial
u^j } = 0 \quad \text{on } (\partial\Omega \backslash M) \times (0, T)$$ $$u(x,0)=0, $$ 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.
ER -