scholarly journals The Cauchy Problem for Thermoelastic Plates with Two Temperatures

2020 ◽  
Vol 39 (1) ◽  
pp. 103-129
Author(s):  
Reinhard Racke ◽  
Yoshihiro Ueda
Keyword(s):  
Cauchy Problem ◽  
Thermoelastic Plates ◽  
The Cauchy Problem ◽  
Two Temperatures

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.

On the Cauchy problem for thermoelastic plates

2006 ◽  
Vol 29 (6) ◽  
pp. 625-636 ◽  
Author(s):  
Igor Chudinovich ◽  
Christian Constanda ◽  
José Colín Venegas
Keyword(s):  
Cauchy Problem ◽  
Thermoelastic Plates ◽  
The Cauchy Problem

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.

Fundamental Serrin type regularity criteria for 3D MHD fluid passing through the porous medium

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1287-1293 ◽  
Author(s):  
Zujin Zhang ◽  
Dingxing Zhong ◽  
Shujing Gao ◽  
Shulin Qiu
Keyword(s):  
Cauchy Problem ◽  
Porous Medium ◽  
Regularity Criterion ◽  
Regularity Criteria ◽  
The Cauchy Problem ◽  
Appl Math

In this paper, we consider the Cauchy problem for the 3D MHD fluid passing through the porous medium, and provide some fundamental Serrin type regularity criteria involving the velocity or its gradient, the pressure or its gradient. This extends and improves [S. Rahman, Regularity criterion for 3D MHD fluid passing through the porous medium in terms of gradient pressure, J. Comput. Appl. Math., 270 (2014), 88-99].

scholarly journals A modified Tikhonov regularization method based on Hermite expansion for solving the Cauchy problem of the Laplace equation

2020 ◽  
Vol 18 (1) ◽  
pp. 1685-1697
Author(s):  
Zhenyu Zhao ◽  
Lei You ◽  
Zehong Meng
Keyword(s):  
Cauchy Problem ◽  
Laplace Equation ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Regularization Parameter ◽  
Solution Process ◽  
Tikhonov Regularization Method ◽  
Hermite Expansion ◽  
The Cauchy Problem ◽  
Ill Posed

Abstract In this paper, a Cauchy problem for the Laplace equation is considered. We develop a modified Tikhonov regularization method based on Hermite expansion to deal with the ill posed-ness of the problem. The regularization parameter is determined by a discrepancy principle. For various smoothness conditions, the solution process of the method is uniform and the convergence rate can be obtained self-adaptively. Numerical tests are also carried out to verify the effectiveness of the method.

Sign in / Sign up

Export Citation Format

Share Document