On the viscosity solutions to a degenerate parabolic differential equation

Asymptotics of viscosity solutions to some doubly nonlinear parabolic equations

“…The main focus of this paper is Trudinger's equation but we will also state some results for a parabolic equation involving the infinity-Laplacian. This is a followup of the works in [4,5].…”

On the viscosity solutions to a class of nonlinear degenerate parabolic differential equations

“…These are contained in this work and, in addition, are included some fully nonlinear operators such as the Pucci operators. Equations such as (1.1) are of great interest and have been studied in great detail in the weak solution setting, see the discussions in the works cited in [1] and [6]. In this context, a study of large time asymptotic behaviour of viscosity solutions to the equations in [1,2] appears in [3].…”

“…We also assume through out that Our proof of the existence of a positive continuous solution to the problem (5.1) involves constructing positive sub-solutions and super-solutions for the problem that are arbitrarily close, in a local sense, to the data specified on the parabolic boundary P T . Existence then follows by using Perron's method [4], see also [1]. Uniqueness is implied by Theorem 4.3.…”

“…A similar quotient type comparison principle was derived for the doubly nonlinear parabolic equations studied in [1,2]. In Sections 5, 6 and 7, we address the existence of positive solutions to (1.1), i.e,…”

A Phragmén–Lindelöf property of viscosity solutions to a class of doubly nonlinear parabolic equations. Bounded case

“…It follows that the solutions of (1.2) and hence, the solutions of (1.1), satisfy a comparison principle, see [2,3,6]. Incidentally, we do not require that Z be defined in all of R, a matter that will be discussed later.…”