On a non-stationary problem in a dihedral angle.~I

E. V. Frolova

Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 22, Tome 188 (1991), pp. 159-177

Résumé

We investigate a boundary value problem for heat equation in the dihedral angle $D_\theta\subset \mathbb{R}^n$ with Neumann condition on one side of the angle and the boundary condition $$ x\frac{\partial u}{\partial t}-\frac{\partial u}{\partial x_2}+h\frac{\partial u}{\partial x_1}+\sum_{j=1}^3b_j\frac{\partial u}{\partial x_j}\bigm|_{\Gamma_{OT}}=\varphi_0, $$ (where $x>0$, $h\leqslant0$, $b_j$ are real constants) on another side. Unique solvability in weighted Sobolev spaces is proved.