Abstract:
The first mixed problem with homogeneous Dirichlet boundary condition and initial function with compact support is considered for quasilinear second order parabolic equations in a cylindrical domain $D=(0,\infty)\times\Omega$. Upper bounds are obtained, which give the rate of decay of the solutions as $t\to\infty$ as a function of the geometry of the unbounded domain $\Omega\subset \mathbb R_n$, $n\geqslant 2$.
Bibliography: 18 titles.
Keywords:first mixed problem, quasilinear parabolic equations, unbounded domain, stabilization of the solution, geometric characteristic.
Fulltext:
PDF file (632 kB)
