scholarly journals Well-posedness for Hardy–Hénon parabolic equations with fractional Brownian noise

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Mohamed Majdoub ◽  
Ezzedine Mliki
Keyword(s):  
Parabolic Equations ◽  
Well Posedness ◽  
Brownian Noise ◽  
Fractional Brownian Noise

scholarly journals Further results on a space-time FOSLS formulation of parabolic PDEs

2020 ◽  
Author(s):  
Gregor Gantner ◽  
Rob Stevenson
Keyword(s):  
Finite Element Method ◽  
Least Squares ◽  
Parabolic Equations ◽  
Space Time ◽  
Adaptive Finite Element Method ◽  
Order System ◽  
Well Posedness ◽  
Adaptive Finite Element ◽  
Parabolic Pdes ◽  
First Order

In [2019, Space-time least-squares finite elements for parabolic equations, arXiv:1911.01942] by Führer&Karkulik, well-posedness of a space-time First-Order System Least-Squares formulation of the heat equation was proven.  In the present work, this result is generalized to general second order parabolic PDEs with possibly inhomogenoeus boundary conditions, and plain convergence of a standard adaptive finite element method driven by the least-squares estimator is demonstrated.  The proof of the latter easily extends to a large class of least-squares formulations.

scholarly journals A semidiscrete Galerkin scheme for a coupled two-scale elliptic–parabolic system: well-posedness and convergence approximation rates

2020 ◽  
Vol 60 (4) ◽  
pp. 999-1031
Author(s):  
Martin Lind ◽  
Adrian Muntean ◽  
Omar Richardson
Keyword(s):  
Parabolic Equations ◽  
Spatial Scales ◽  
A Priori ◽  
Coupled System ◽  
Scale Model ◽  
Reactive Flow ◽  
Well Posedness ◽  
Approximation Rates ◽  
Priori Error Estimates ◽  
Model Equations

AbstractIn this paper, we study the numerical approximation of a coupled system of elliptic–parabolic equations posed on two separated spatial scales. The model equations describe the interplay between macroscopic and microscopic pressures in an unsaturated heterogeneous medium with distributed microstructures as they often arise in modeling reactive flow in cementitious-based materials. Besides ensuring the well-posedness of our two-scale model, we design two-scale convergent numerical approximations and prove a priori error estimates for the semidiscrete case. We complement our analysis with simulation results illustrating the expected behaviour of the system.

scholarly journals Space-Time Estimates of Mild Solutions of a Class of Higher-Order Semilinear Parabolic Equations in Lp

2014 ◽  
Vol 1 (1) ◽  
Author(s):  
Albert N. Sandjo ◽  
Célestin Wafo Soh
Keyword(s):  
Thin Film ◽  
Epitaxial Growth ◽  
Parabolic Equations ◽  
Mild Solutions ◽  
Film Theory ◽  
Well Posedness ◽  
Semilinear Parabolic Equations ◽  
Unified Framework ◽  
Time Estimates ◽  
Semilinear Parabolic

AbstractWe establish the well-posedness of boundary value problems for a family of nonlinear higherorder parabolic equations which comprises some models of epitaxial growth and thin film theory. In order to achieve this result, we provide a unified framework for constructing local mild solutions in C

On modes of long-range dependence

2002 ◽  
Vol 39 (4) ◽  
pp. 882-888 ◽  
Author(s):  
C. C. Heyde
Keyword(s):  
Long Range ◽  
Weak Dependence ◽  
Risky Asset ◽  
Long Range Dependence ◽  
Brownian Noise ◽  
Fractional Brownian Noise

This paper aims at enhancing the understanding of long-range dependence (LRD) by focusing on mechanisms for generating this dependence, namely persistence of signs and/or persistence of magnitudes beyond what can be expected under weak dependence. These concepts are illustrated through a discussion of fractional Brownian noise of index H ∈ (0,1) and it is shown that LRD in signs holds if and only if ½ < H < 1 and LRD in magnitudes if and only if ¾ ≤ H < 1. An application to discrimination between two risky asset finance models, the FATGBM model of Heyde and the multifractal model of Mandelbrot, is given to illustrate the use of the ideas.

scholarly journals Well-Posedness of Nonlocal Parabolic Differential Problems with Dependent Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Asker Hanalyev
Keyword(s):  
Differential Equation ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Continuous Functions ◽  
Parabolic Differential Equation ◽  
Well Posedness ◽  
Nonlocal Boundary Value Problem ◽  
Hölder Condition ◽  
Linear Positive Operator

The nonlocal boundary value problem for the parabolic differential equationv'(t)+A(t)v(t)=f(t)  (0≤t≤T),  v(0)=v(λ)+φ,  0<λ≤Tin an arbitrary Banach spaceEwith the dependent linear positive operatorA(t)is investigated. The well-posedness of this problem is established in Banach spacesC0β,γ(Eα-β)of allEα-β-valued continuous functionsφ(t)on[0,T]satisfying a Hölder condition with a weight(t+τ)γ. New Schauder type exact estimates in Hölder norms for the solution of two nonlocal boundary value problems for parabolic equations with dependent coefficients are established.

scholarly journals On the Second Order of Accuracy Stable Implicit Difference Scheme for Elliptic-Parabolic Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Allaberen Ashyralyev ◽  
Okan Gercek
Keyword(s):  
Difference Scheme ◽  
Parabolic Equations ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Approximate Solutions ◽  
Second Order ◽  
Well Posedness ◽  
Parabolic Differential Equations ◽  
Implicit Difference Scheme ◽  
Order Of Accuracy

We are interested in studying a second order of accuracy implicit difference scheme for the solution of the elliptic-parabolic equation with the nonlocal boundary condition. Well-posedness of this difference scheme is established. In an application, coercivity estimates in Hölder norms for approximate solutions of multipoint nonlocal boundary value problems for elliptic-parabolic differential equations are obtained.

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