scholarly journals A General Decay and Optimal Decay Result in a Heat System with a Viscoelastic Term

2019 ◽  
Vol 39 (2) ◽  
pp. 618-626
Author(s):  
Abderrahmane Youkana ◽  
Salim A. Messaoudi ◽  
Aissa Guesmia
Author(s):  
Mohammad Shahrouzi ◽  
Jorge Ferreira ◽  
Erhan Pişkin

In this paper we consider a viscoelastic double-Kirchhoff type wave equation of the form $$ u_{tt}-M_{1}(\|\nabla u\|^{2})\Delta u-M_{2}(\|\nabla u\|_{p(x)})\Delta_{p(x)}u+(g\ast\Delta u)(x,t)+\sigma(\|\nabla u\|^{2})h(u_{t})=\phi(u), $$ where the functions $M_{1},M_{2}$ and $\sigma, \phi$ are real valued functions and $(g\ast\nabla u)(x,t)$ is the viscoelastic term which are introduced later. Under appropriate conditions for the data and exponents, the general decay result and blow-up of solutions are proved with positive initial energy. This study extends and improves the previous results in the literature to viscoelastic double-Kirchhoff type equation with degenerate nonlocal damping and variable-exponent nonlinearities.


2006 ◽  
Author(s):  
Paul E. O'Connor ◽  
Dale Hyde ◽  
Demetri Economos ◽  
Rene Beck
Keyword(s):  

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Soh Edwin Mukiawa ◽  
Cyril Dennis Enyi ◽  
Tijani Abdulaziz Apalara

AbstractWe investigate a thermoelastic Bresse system with viscoelastic damping acting on the shear force and heat conduction acting on the bending moment. We show that with weaker conditions on the relaxation function and physical parameters, the solution energy has general and optimal decay rates. Some examples are given to illustrate the findings.


Resources ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 31
Author(s):  
Stanislav Jacko ◽  
Roman Farkašovský ◽  
Igor Ďuriška ◽  
Barbora Ščerbáková ◽  
Kristína Bátorová

The Pannonian basin is a major geothermal heat system in Central Europe. Its peripheral basin, the East Slovakian basin, is an example of a geothermal structure with a linear, directed heat flow ranging from 90 to 100 mW/m2 from west to east. However, the use of the geothermal source is limited by several critical tectono-geologic factors: (a) Tectonics, and the associated disintegration of the aquifer block by multiple deformations during the pre-Paleogene, mainly Miocene, period. The main discontinuities of NW-SE and N-S direction negatively affect the permeability of the aquifer environment. For utilization, minor NE-SW dilatation open fractures are important, which have been developed by sinistral transtension on N–S faults and accelerated normal movements to the southeast. (b) Hydrogeologically, the geothermal structure is accommodated by three water types, namely, Na-HCO3 with 10.9 g·L−1 mineralization (in the north), the Ca-Mg-HCO3 with 0.5–4.5 g·L−1 mineralization (in the west), and Na-Cl water type containing 26.8–33.4 g·L−1 mineralization (in the southwest). The chemical composition of the water is influenced by the Middle Triassic dolomite aquifer, as well as by infiltration of saline solutions and meteoric waters along with open fractures/faults. (c) Geothermally anomalous heat flow of 123–129 °C with 170 L/s total flow near the Slanské vchy volcanic chain seems to be the perspective for heat production.


2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mohammad M. Al-Gharabli ◽  
Adel M. Al-Mahdi ◽  
Salim A. Messaoudi

Abstract This work is concerned with a system of two singular viscoelastic equations with general source terms and nonlocal boundary conditions. We discuss the stabilization of this system under a very general assumption on the behavior of the relaxation function $k_{i}$ k i , namely, $$\begin{aligned} k_{i}^{\prime }(t)\le -\xi _{i}(t) \Psi _{i} \bigl(k_{i}(t)\bigr),\quad i=1,2. \end{aligned}$$ k i ′ ( t ) ≤ − ξ i ( t ) Ψ i ( k i ( t ) ) , i = 1 , 2 . We establish a new general decay result that improves most of the existing results in the literature related to this system. Our result allows for a wider class of relaxation functions, from which we can recover the exponential and polynomial rates when $k_{i}(s) = s^{p}$ k i ( s ) = s p and p covers the full admissible range $[1, 2)$ [ 1 , 2 ) .


2021 ◽  
Vol 500 (1) ◽  
pp. 125136
Author(s):  
Adel M. Al-Mahdi ◽  
Mohammad M. Al-Gharabli ◽  
Salim A. Messaoudi

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