The limit of vanishing viscosity for doubly nonlinear parabolic equations

作者：Matas Ales; Merker Jochen^*

来源：Electronic Journal of Qualitative Theory of Differential Equations, 2014, (8): 1-14.

DOI：10.14232/ejqtde.2014.1.8

• vanishing viscosity
• doubly nonlinear evolution equations
• conservation law
• quasilinear
• degenerate

We show that solutions of the doubly nonlinear parabolic equation %26lt;br%26gt;partial derivative b(u)/partial derivative t - epsilon div(a(del u)) + div (f(u)) = g %26lt;br%26gt;converge in the limit epsilon SE arrow 0 of vanishing viscosity to an entropy solution of the doubly nonlinear hyperbolic equation %26lt;br%26gt;partial derivative b(u)/partial derivative t + div (f(u)) = g. %26lt;br%26gt;The difficulty here lies in the fact that the functions a and b specifying the diffusion are nonlinear.

• 出版日期2014