An Existence Result for Superparabolic Functions
نویسندگان
چکیده
We study superparabolic functions related to nonlinear parabolic equations. They are de ned by means of a parabolic comparison principle with respect to solutions. We show that every superparabolic function satis es the equation with a positive Radon measure on the right-hand side, and conversely, for every nite positive Radon measure there exists a superparabolic function which is solution to the corresponding equation with measure data.
منابع مشابه
Nonlinear Parabolic Capacity and Polar Sets of Superparabolic Functions
We extend the theory of the thermal capacity for the heat equation to nonlinear parabolic equations of the p-Laplacian type. We study definitions and properties of the nonlinear parabolic capacity and show that the capacity of a compact set can be represented via a capacitary potential. As an application, we show that polar sets of superparabolic functions are of zero capacity. The main technic...
متن کاملOn the Equivalence of Viscosity Solutions and Weak Solutions for a Quasi-Linear Equation
We discuss and compare various notions of weak solution for the p-Laplace equation −div(|∇u|p−2∇u) = 0 and its parabolic counterpart ut − div(|∇u|p−2∇u) = 0. In addition to the usual Sobolev weak solutions based on integration by parts, we consider the p-superharmonic (or p-superparabolic) functions from nonlinear potential theory and the viscosity solutions based on generalized pointwise deriv...
متن کاملEFFICIENCY EVALUATION OF PROPOSED OBJECTIVE FUNCTIONS IN STRUCTURAL DAMAGE DETECTION BASED ON MODAL STRAIN ENERGY AND FLEXIBILITY APPROACHES
Civil infrastructures such as bridges and buildings are prone to damage as a result of natural disasters. To understand damages induced by these events, the structure needs to be monitored. The field of engineering focusing on the process of evaluating the location and the intensity of the damage to the structure is called Structural Health Monitoring (SHM). Early damage prognosis in structures...
متن کاملExistence and uniqueness of common coupled fixed point results via auxiliary functions
The purpose of this paper is to establish some coupled coincidence point theorems for mappings having a mixed $g$-monotone property in partially ordered metric spaces. Also, we present a result on the existence and uniqueness of coupled common fixed points. The results presented in the paper generalize and extend several well-known results in the literature.
متن کاملSEMIGROUP ACTIONS , WEAK ALMOST PERIODICITY, AND INVARIANT MEANS
Let S be a topological semigroup acting on a topological space X. We develop the theory of (weakly) almost periodic functions on X, with respect to S, and form the (weakly) almost periodic compactifications of X and S, with respect to each other. We then consider the notion of an action of Son a Banach space, and on its dual, and after defining S-invariant means for such a space, we give a...
متن کامل