scholarly journals Lp-Lq time decay estimate to the solution of the Cauchy problem of the system of equations for nonlocal model of hyperbolic thermoelasticity theory

PAMM ◽  
2008 ◽  
Vol 8 (1) ◽  
pp. 10497-10498 ◽  
Author(s):  
Jerzy Gawinecki ◽  
Jaroslaw Lazuka ◽  
Jozef Rafa
Keyword(s):  
Cauchy Problem ◽  
Decay Estimate ◽  
System Of Equations ◽  
Nonlocal Model ◽  
Time Decay ◽  
Hyperbolic Thermoelasticity ◽  
Thermoelasticity Theory ◽  
The Cauchy Problem

scholarly journals Remarks on the Systems of Semilinear Fractional Rayleigh-Stokes Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Le Dinh Long
Keyword(s):  
Cauchy Problem ◽  
Fourier Analysis ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Newtonian Fluids ◽  
System Of Equations ◽  
Main Technique ◽  
The Cauchy Problem ◽  
The Stability

In this paper, we study the Cauchy problem for a system of Rayleigh-Stokes equations. In this system of equations, we use derivatives in the classical Riemann-Liouville sense. This system has many applications in some non-Newtonian fluids. We obtained results for the existence, uniqueness, and frequency of the solution. We discuss the stability of the solutions and find the solution spaces. Our main technique is to use the Banach mapping theorem combined with some techniques in Fourier analysis.

LANDAU–GINZBURG TYPE EQUATIONS IN THE SUBCRITICAL CASE

2003 ◽  
Vol 05 (01) ◽  
pp. 127-145 ◽  
Author(s):  
NAKAO HAYASHI ◽  
ELENA I. KAIKINA ◽  
PAVEL I. NAUMKIN
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Decay Rate ◽  
Unique Solution ◽  
Linear Case ◽  
Decay Estimates ◽  
Time Decay ◽  
Subcritical Case ◽  
Small Norm ◽  
The Cauchy Problem

We study the Cauchy problem for the nonlinear Landau–Ginzburg equation [Formula: see text] where α, β ∈ C with dissipation condition ℜα > 0. We are interested in the subcritical case [Formula: see text]. We assume that θ = | ∫ u0(x) dx| ≠ 0 and ℜδ (α, β) > 0, where [Formula: see text] Furthermore we suppose that the initial data u0 ∈ L1 are such that (1+|x|)au0 ∈ L1, with sufficiently small norm ε = ‖(1 + |x|)a u0 ‖1, where a ∈ (0,1). Also we assume that σ is sufficiently close to [Formula: see text]. Then there exists a unique solution of the Cauchy problem (*) such that [Formula: see text] satisfying the following time decay estimates for large t > 0[Formula: see text] Note that in comparison with the corresponding linear case the decay rate of the solutions of (*) is more rapid.

scholarly journals THE CAUCHY PROBLEM FOR THE SYSTEM OF EQUATIONS OF THERMOELASTICITY IN E^n

2014 ◽  
Vol 15 (1) ◽  
Author(s):  
Ikbol E. Niyozov ◽  
O. I. Makhmudov
Keyword(s):  
Cauchy Problem ◽  
Bounded Domain ◽  
Analytical Continuation ◽  
System Of Equations ◽  
The Cauchy Problem

ABSTRACT: In this paper we consider the problem of analytical continuation of solutions to the system of equations of thermoelasticity in a bounded domain from their values and values of their strains on a part of the boundary of this domain, i.e., we study the Cauchy problem. ABSTRAK: Di dalam kajian ini, kami menyelidiki masalah keselanjaran analitik bagi penyelesaian-penyelesaian terhadap sistem persamaan-persamaan termoelastik di dalam domain bersempadan berdasarkan nilai-nilainya dan nilai tegasannya bagi sebahagian daripada sempadan domain tersebut, iaitu kami mengkaji masalah Cauchy.

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