Decay of mass for fractional evolution equation with memory term
نویسنده
چکیده
The decay properties of the mass M(t) = ∫ RN u(·, t)dx of the solutions of a fractional diffusion equation with nonlinear memory term is studied. For a suitable class of initial data and a restriction on the diffusion and nonlinear term, we show that the memory term determines the large time asymptotics, precisely, M(t) tends to zero as t→∞. AMS subject classifications: Primary: 35K55; Secondary: 35B40.
منابع مشابه
Existence of Mild Solutions to a Cauchy Problem Presented by Fractional Evolution Equation with an Integral Initial Condition
In this article, we apply two new fixed point theorems to investigate the existence of mild solutions for a nonlocal fractional Cauchy problem with an integral initial condition in Banach spaces.
متن کاملMagnetohydrodynamic Free Convection Flows with Thermal Memory over a Moving Vertical Plate in Porous Medium
The unsteady hydro-magnetic free convection flow with heat transfer of a linearly viscous, incompressible, electrically conducting fluid near a moving vertical plate with the constant heat is investigated. The flow domain is the porous half-space and a magnetic field of a variable direction is applied. The Caputo time-fractional derivative is employed in order to introduce a thermal flux consti...
متن کاملUpscaling chemical reactions in multicontinuum systems: When might time fractional equations work?
It may often be tempting to take a fractional diffusion equation and simply create a fractional reactiondiffusion equation by including an additional reaction term of the same form as one would include for a standard Fickian system. However, in real systems, fractional diffusion equations typically arise due to complexity and heterogeneity at some unresolved scales. Thus, while transport of a c...
متن کاملElectro-magneto-hydrodynamics Flows of Burgers' Fluids in Cylindrical Domains with Time Exponential Memory
This paper investigates the axial unsteady flow of a generalized Burgers’ fluid with fractional constitutive equation in a circular micro-tube, in presence of a time-dependent pressure gradient and an electric field parallel to flow direction and a magnetic field perpendicular on the flow direction. The mathematical model used in this work is based on a time-nonlocal constitutive equation for s...
متن کاملAiry equation with memory involvement via Liouville differential operator
In this work, a non-integer order Airy equation involving Liouville differential operator is considered. Proposing an undetermined integral solution to the left fractional Airy differential equation, we utilize some basic fractional calculus tools to clarify the closed form. A similar suggestion to the right FADE, converts it into an equation in the Laplace domain. An illustration t...
متن کامل