5 research outputs found
Large Time Behavior of Solutions to the Neumann Problem for a Quasilinear Second Order Degenerate Parabolic Equation in Domains with Noncompact Boundary
AbstractWe investigate the optimal rate of stabilization at large time of a solution to the Neumann problemut=âi=1Nââxi(ai(x, t, âu))âb(x, t, u),inΩĂ(0, T),T>0âi=1Nai(x, t, âu)ni=0,onâΩĂ(0, T)u(x, 0)=u0(x)xâΩ,u0(x)â©Ÿ0inΩ,where ΩâRN, Nâ©Ÿ2, is an unbounded domain with sufficiently smooth noncompact boundary âΩ satisfying certain isoperimetrical inequality and n=(ni) is the outward normal to âΩ