Convergence to Steady States for a One-dimensional Viscous Hamilton-jacobi Equation with Dirichlet Boundary Conditions
نویسنده
چکیده
The convergence to steady states of non-negative solutions u to the one-dimensional viscous Hamilton-Jacobi equation ∂tu − ∂2 xu = |∂xu|, (t, x) ∈ (0,∞)× (−1, 1) with homogeneous Dirichlet boundary conditions is investigated. For that purpose, a Liapunov functional is constructed by the approach of Zelenyak (1968). Instantaneous extinction of ∂xu on a subinterval of (−1, 1) is also shown for suitable initial data. The convergence towards steady states of sign-changing solutions is also considered. MSC 2000: 35B35, 35K55
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تاریخ انتشار 2005