Qualitative Properties of Monotone Linear Parabolic Operators
نویسندگان
چکیده
When we construct mathematical or numerical models in order to solve a real-life problem, it is important to preserve the characteristic properties of the original process. The models have to possess the equivalents of these properties. Parabolic partial equations generally serve as the mathematical models of heat conduction or diffusion processes, where the most important properties are the monotonicity, the nonnegativity preservation and the maximum principles. In this paper, the validity of the equivalents of these qualitative properties are investigated for the second order linear partial differential operator. Conditions are given that guarantee the qualitative properties. On some examples we investigate these conditions.
منابع مشابه
Some Remarks on a General Construction of Approximation Processes
The aim of this paper is to study the characteristics of a general method to produce a new approximation sequence from a given one, by using suitable convex combinations, whose coefficients depend on some functions λn (n ≥ 1). This type of construction was first used to generate Lototsky-Schnabl operators from Bernstein operators (see section 6.1. in [1]) and turned to be really useful in the s...
متن کاملA caricature of a singular curvature flow in the plane
We study a singular parabolic equation of the total variation type in one dimension. The problem is a simplification of the singular curvature flow. We show existence and uniqueness of weak solutions. We also prove existence of weak solutions to the semi-discretization of the problem as well as convergence of the approximating sequences. The semi-discretization shows that facets must form. For ...
متن کاملSome results on pre-monotone operators
In this paper, some properties of pre-monotone operators are proved. It is shown that in a reflexive Banach space, a full domain multivalued $sigma$-monotone operator with sequentially norm$times$weak$^*$ closed graph is norm$times$weak$^*$ upper semicontinuous. The notion of $sigma$-convexity is introduced and the relations between the $sigma$-monotonicity and $sigma$-convexity is i...
متن کاملLinear stability analysis of travelling waves for a pseudo-parabolic Burgers’ equation
We investigate the linear stability of non-monotone travelling wave solutions of the pseudo-parabolic Burgers’ type equation ∂u ∂t = ∂u ∂x2 + 2u ∂u ∂x + τ ∂u ∂x2∂t with τ > 0 . The monotonicity of the waves depending on the strength of the parameter τ and the far-filed values. The most part of the paper is devoted to prove that the linear stability is determined by the spectrum of the linearise...
متن کاملA SYSTEM OF GENERALIZED VARIATIONAL INCLUSIONS INVOLVING G-eta-MONOTONE MAPPINGS
We introduce a new concept of general $G$-$eta$-monotone operator generalizing the general $(H,eta)$-monotone operator cite{arvar2, arvar1}, general $H-$ monotone operator cite{xiahuang} in Banach spaces, and also generalizing $G$-$eta$-monotone operator cite{zhang}, $(A, eta)$-monotone operator cite{verma2}, $A$-monotone operator cite{verma0}, $(H, eta)$-monotone operator cite{fanghuang}...
متن کامل