Please use this identifier to cite or link to this item:
|Title:||Generalized Viscosity Solutions of Fully Non-linear Parabolic Equations with Distributions as Initial Conditions|
|Publisher:||Published in European Journal of Scientific Research|
|Abstract:||Consider the fully nonlinear parabolic problem u (D u,Du,u,x,t) 0 Q 0,T T 0 2 t f u u (x) Q 0 2 10 where i j i 2 2 t x u, Du x x u, D u t uu . is a bounded open set in Rn and Zn is a positive integer. If u (x) 0 is a distribution with compact support, it is well known that the classical theory for viscosity solutions does not cover the case where f is discontinuous. This is because the straight forward method of comparing sub and super solutions does not work if f is discontinuous with respect to x and t. We obtain existence and uniqueness results for this class of problems by introducing the concept of Generalized Viscosity Solutions valid in the general case in which the equations are elements of the space of Generalized Functions. No linearization of the equations is assumed, that is our theory is fully non-linear. The solutions thus obtained are shown to be consistent with the classical distributional solutions whenever they exist.|
|Appears in Collections:||Abstracts|
Files in This Item:
|Generalized_Viscosity_Solutions_of_Fully_Non-linear_Parabolic_Equations.pdf||83.1 kB||Adobe PDF||View/Open|
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.