On Existence of Local Solutions for a Hyperbolic System Modelling Chemotaxis with Memory Term

2021 ◽  
Vol 34 (2) ◽  
pp. 170-185
Author(s):  
Wu Shaohua & Wang Pengfei
Keyword(s):  
Hyperbolic System ◽  
Memory Term ◽  
System Modelling ◽  
Local Solutions ◽  
With Memory

scholarly journals Exponential Attractors for the 3D Fractional-order Bardina Turbulence Model With Memory and Horizontal Filtering

2021 ◽  
Author(s):  
Michele Annese ◽  
Luca Bisconti ◽  
Davide Catania
Keyword(s):  
Phase Space ◽  
Fractional Order ◽  
Turbulence Model ◽  
Memory Term ◽  
Exponential Attractor ◽  
Exponential Attractors ◽  
Regularity Properties ◽  
Hereditary Effects ◽  
With Memory ◽  
Simplified Bardina

AbstractWe consider the 3D simplified Bardina turbulence model with horizontal filtering, fractional dissipation, and the presence of a memory term incorporating hereditary effects. We analyze the regularity properties and the dissipative nature of the considered system and, in our main result, we show the existence of a global exponential attractor in a suitable phase space.

Walrasian Equilibrium Problem with Memory Term

2011 ◽  
Vol 151 (1) ◽  
pp. 64-80 ◽  
Author(s):  
Maria Bernadette Donato ◽  
Monica Milasi ◽  
Laura Scrimali
Keyword(s):  
Equilibrium Problem ◽  
Walrasian Equilibrium ◽  
Memory Term ◽  
With Memory

DECAY PROPERTY FOR THE TIMOSHENKO SYSTEM WITH MEMORY-TYPE DISSIPATION

2012 ◽  
Vol 22 (02) ◽  
pp. 1150012 ◽  
Author(s):  
YONGQIN LIU ◽  
SHUICHI KAWASHIMA
Keyword(s):  
Decay Estimate ◽  
Pointwise Estimate ◽  
Decay Property ◽  
Memory Term ◽  
Fourier Space ◽  
Initial Value ◽  
Timoshenko System ◽  
Frictional Dissipation ◽  
Memory Type ◽  
With Memory

In this paper we consider the initial value problem for the Timoshenko system with a memory term. We construct the fundamental solution by using the Fourier–Laplace transform and obtain the solution formula of the problem. Moreover, applying the energy method in the Fourier space, we derive the pointwise estimate of solutions in the Fourier space, which gives a sharp decay estimate of solutions. It is shown that the decay property of the system is of the regularity-loss type and is weaker than that of the Timoshenko system with a frictional dissipation.

Local solvability of an inverse problem to the Navier–Stokes equation with memory term

2020 ◽  
Vol 36 (6) ◽  
pp. 065007
Author(s):  
Yu Jiang ◽  
Jishan Fan ◽  
Sei Nagayasu ◽  
Gen Nakamura
Keyword(s):  
Inverse Problem ◽  
Stokes Equation ◽  
Local Solvability ◽  
Navier Stokes ◽  
Memory Term ◽  
Navier Stokes Equation ◽  
With Memory

scholarly journals Decay of mass for fractional evolution equation with memory term

2012 ◽  
Vol 71 (2) ◽  
pp. 215-228 ◽  
Author(s):  
Ahmad Z. Fino ◽  
Hassan Ibrahim ◽  
Bilal Barakeh
Keyword(s):  
Evolution Equation ◽  
Memory Term ◽  
Fractional Evolution Equation ◽  
With Memory
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