Convergence to steady states for a one-dimensional viscous Hamilton¿Jacobi equation with Dirichlet boundary conditions

• Autores: Philippe Laurençot
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 230, Nº 2, 2007, págs. 347-364
• Idioma: inglés
• DOI: 10.2140/pjm.2007.230.347
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• Resumen

  • We investigate the convergence to steady states of the solutions to the one-dimensional viscous Hamilton¿Jacobi equation ?tu - ?x2u = |?xu|p, where (t,x) in (0,8) × (-1,1) and p in (0,1), with homogeneous Dirichlet boundary conditions. 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 shown for suitable initial data.