Maximal Regularity for Fractional Cauchy Equation in Hölder Space and Its Approximation

2019 ◽  
Vol 19 (4) ◽  
pp. 779-796 ◽  
Author(s):  
Li Liu ◽  
Zhenbin Fan ◽  
Gang Li ◽  
Sergey Piskarev
Keyword(s):  
Cauchy Problem ◽  
Maximal Regularity ◽  
Well Posedness ◽  
Cauchy Equation ◽  
Holder Space ◽  
Hölder Space ◽  
Implicit Difference Schemes ◽  
Existence And Stability ◽  
Fractional Cauchy Problem ◽  
Resolvent Families

AbstractWe derive the well-posedness and maximal regularity of the fractional Cauchy problem in Hölder space {C_{0}^{\gamma}(E)}. We also obtain the existence and stability of new implicit difference schemes for the general approximation to the nonhomogeneous fractional Cauchy problem. Our analysis is based on the approaches of the theory of β-resolvent families, functional analysis and numerical analysis.

scholarly journals Lp-Lq-Well Posedness for the Moore–Gibson–Thompson Equation with Two Temperatures on Cylindrical Domains

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1748
Author(s):  
Carlos Lizama ◽  
Marina Murillo-Arcila
Keyword(s):  
Cauchy Problem ◽  
Sound Propagation ◽  
Maximal Regularity ◽  
Fourier Multipliers ◽  
Well Posedness ◽  
Elastic Media ◽  
Regularity Estimates ◽  
The Cauchy Problem ◽  
Cylindrical Domains ◽  
Two Temperatures

We examine the Cauchy problem for a model of linear acoustics, called the Moore–Gibson–Thompson equation, describing a sound propagation in thermo-viscous elastic media with two temperatures on cylindrical domains. For an adequate combination of the parameters of the model we prove Lp-Lq-well-posedness, and we provide maximal regularity estimates which are optimal thanks to the theory of operator-valued Fourier multipliers.

Orbital stability of standing waves of a class of fractional Schrödinger equations with Hartree-type nonlinearity

2016 ◽  
Vol 15 (05) ◽  
pp. 699-729 ◽  
Author(s):  
Yonggeun Cho ◽  
Mouhamed M. Fall ◽  
Hichem Hajaiej ◽  
Peter A. Markowich ◽  
Saber Trabelsi
Keyword(s):  
Cauchy Problem ◽  
Standing Waves ◽  
Orbital Stability ◽  
Schrodinger Equations ◽  
Well Posedness ◽  
Concentration Compactness ◽  
Schrödinger Equations ◽  
Fractional Schrödinger Equations ◽  
Nonlinear Fractional Schrödinger Equations ◽  
Existence And Stability

This paper is devoted to the mathematical analysis of a class of nonlinear fractional Schrödinger equations with a general Hartree-type integrand. We show the well-posedness of the associated Cauchy problem and prove the existence and stability of standing waves under suitable assumptions on the nonlinearity. Our proofs rely on a contraction argument in mixed functional spaces and the concentration-compactness method.

scholarly journals Well-posedness of boundary value problems for reverse parabolic equation with integral condition

2018 ◽  
Vol 1 (1) ◽  
pp. 11-21
Author(s):  
Charyyar Ashyralyyev
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problems ◽  
Parabolic Problem ◽  
Boundary Value ◽  
Integral Condition ◽  
Stability Estimates ◽  
Well Posedness ◽  
Holder Space ◽  
Hölder Space ◽  
Coercive Stability

AbstractReverse parabolic equation with integral condition is considered. Well-posedness of reverse parabolic problem in the Hölder space is proved. Coercive stability estimates for solution of three boundary value problems (BVPs) to reverse parabolic equation with integral condition are established.

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

The weighted Cauchy problem for linear functional differential equations with strong singularities

2011 ◽  
Vol 18 (3) ◽  
pp. 577-586
Author(s):  
Zaza Sokhadze
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Initial Point ◽  
Higher Order ◽  
Well Posedness ◽  
Deviating Arguments ◽  
Functional Differential

Abstract The sufficient conditions of well-posedness of the weighted Cauchy problem for higher order linear functional differential equations with deviating arguments, whose coefficients have nonintegrable singularities at the initial point, are found.

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