Search results for "Semigroup"

A bending theory of thermoelastic diffusion plates based on Green-Naghdi theory

2017

Abstract This article is concerned with bending plate theory for thermoelastic diffusion materials under Green-Naghdi theory. First, we present the basic equations which characterize the bending of thin thermoelastic diffusion plates for type II and III models. The theory allows for the effect of transverse shear deformation without any shear correction factor, and permits the propagation of waves at a finite speed without energy dissipation for type II model and with energy dissipation for type III model. By the semigroup theory of linear operators, we prove the well-posedness of the both models and the asymptotic behavior of the solutions of type III model. For unbounded plate of type III…

Existence and Regularity for a Class of Nonlinear Hyperbolic Boundary Value Problems

2002

AbstractThe regularity of the solution of the telegraph system with nonlinear monotone boundary conditions is investigated by two methods. The first one is based on D'Alembert-type representation formulae for the solution. In the second method the telegraph system is reduced to a linear Cauchy problem with a locally Lipschitzian functional perturbation; then regularity results are established by appealing to the theory of linear semigroups.

Pseudocomplements in sum-ordered partial semirings

2007

We study a particular way of introducing pseudocomplementation in ordered semigroups with zero, and characterise the class of those pseudocomplemented semigroups, termed g-semigroups here, that admit a Glivenko type theorem (the pseudocomplements form a Boolean algebra). Some further results are obtained for g-semirings – those sum-ordered partially additive semirings whose multiplicative part is a g-semigroup. In particular, we introduce the notion of a partial Stone semiring and show that several well-known elementary characteristics of Stone algebras have analogues for such semirings.

The ideal duplication

2021

AbstractIn this paper we present and study the ideal duplication, a new construction within the class of the relative ideals of a numerical semigroup S, that, under specific assumptions, produces a relative ideal of the numerical duplication $$S\bowtie ^b E$$ S ⋈ b E . We prove that every relative ideal of the numerical duplication can be uniquely written as the ideal duplication of two relative ideals of S; this allows us to better understand how the basic operations of the class of the relative ideals of $$S\bowtie ^b E$$ S ⋈ b E work. In particular, we characterize the ideals E such that $$S\bowtie ^b E$$ S ⋈ b E is nearly Gorenstein.

Permutation properties and the fibonacci semigroup

1989

Dissipative operators and differential equations on Banach spaces

1991

If we consider the initial value problem Inline Equation $$x'(t) = f(t,x(t)),{\text{ }}x(0) = {x_0}$$ on the real line, it is well known that one—sided bounds like Inline Equation $$\left[ {f(t,x) - f\left( {t,y} \right)} \right]\left( {x - {\text{y}}} \right) \leqslant \omega {\left( {x - y} \right)^2}$$ give much better information about the behaviour of solutions than the Lipschitz- type estimates Inline Equation $$ \left| {f\left( {t,x} \right) - f\left( {t,y} \right)} \right| \leqslant L\left| {x - y} \right|,$$ because ω, unlike L, may be negative.

Nonlocal Heat Content

2019

The heat content of a Borel measurable set \(D \subset \mathbb {R}^N\) at time t is defined by M. van der Berg in [69] (see also [70]) as: $$\displaystyle \mathbb {H}_D(t) = \int _D T(t) {\chi }_D (x) dx, $$ with (T(t))t≥0 being the heat semigroup in \(L^2(\mathbb {R}^N)\). Therefore, the heat content represents the amount of heat in D at time t if in D the initial temperature is 1 and in \(\mathbb {R}^N \setminus D\) the initial temperature is 0.

Weak convergence theorems for asymptotically nonexpansive mappings and semigroups

2001

Levy targeting and the principle of detailed balance

2011

We investigate confining mechanisms for Lévy flights under premises of the principle of detailed balance. In this case, the master equation of the jump-type process admits a transformation to the Lévy-Schrödinger semigroup dynamics akin to a mapping of the Fokker-Planck equation into the generalized diffusion equation. This sets a correspondence between above two stochastic dynamical systems, within which we address a (stochastic) targeting problem for an arbitrary stability index μ ε (0,2) of symmetric Lévy drivers. Namely, given a probability density function, specify the semigroup potential, and thence the jump-type dynamics for which this PDF is actually a long-time asymptotic (target) …

Existence and uniqueness of a solution for a parabolic quasilinear problem for linear growth functionals with $L^1$ data

2002

We introduce a new concept of solution for the Dirichlet problem for quasilinear parabolic equations in divergent form for which the energy functional has linear growth. Using Kruzhkov's method of doubling variables both in space and time we prove uniqueness and a comparison principle in $L^1$ for these solutions. To prove the existence we use the nonlinear semigroup theory.