Quasilinear parabolic equations with nonlinear boundary conditions

[摘要] Of concern is the following quasilinear parabolic equation with nonlinear boundary conditions: u(t)(x,t) = alpha (x,Du)Deltau + g(x,u,Du) for (x,t) epsilon Omega x (0,infinity) partial derivativeu/partial derivativev + beta (x,u) = 0 for (x,t) epsilon alpha Omega x (0,infinity) u(x,0) = u(0)(x). The diffusion coefficient a can vanish on the spacial boundary at a certain rate. It is shown by a difference scheme from the method of lines that (*) has a unique global strong solution. (C) 2000 Elsevier Science B.V. All rights reserved. MSC: 35A05; 35B35; 35B65.

[发布日期] 2000-12-30

[关键词] method of lines