Refined Asymptotic Expansions of Solutions to Fractional Diffusion Equations
نویسندگان
چکیده
In this paper, as an improvement of the paper (Ishige et al. in SIAM J Math Anal 49:2167–2190, 2017), we obtain higher order asymptotic expansions large time behavior solution to Cauchy problem for inhomogeneous fractional diffusion equations and nonlinear equations.
منابع مشابه
Numerical solutions for fractional reaction-diffusion equations
Fractional diffusion equations are useful for applications where a cloud of particles spreads faster than the classical equation predicts. In a fractional diffusion equation, the second derivative in the spatial variable is replaced by a fractional derivative of order less than two. The resulting solutions spread faster than the classical solutions and may exhibit asymmetry, depending on the fr...
متن کاملAsymptotic Expansions for Nonlocal Diffusion
We study the asymptotic behavior for solutions to nonlocal diffusion models of the form ut = J ∗ u − u in the whole R with an initial condition u(x, 0) = u0(x). Under suitable hypotheses on J (involving its Fourier transform) and u0, it is proved an expansion of the form ∥∥u(u)− ∑ |α|≤k (−1)|α| α! ( ∫ u0(x)x dx ) ∂Kt ∥∥ Lq(Rd) ≤ Ct−A, where Kt is the regular part of the fundamental solution and...
متن کاملResearch Paper Asymptotic Estimates of Solutions to Initial-boundary-value Problems for Distributed Order Time-fractional Diffusion Equations
This article deals with investigation of some important properties of solutions to initial-boundary-value problems for distributed order timefractional diffusion equations in bounded multi-dimensional domains. In particular, we investigate the asymptotic behavior of the solutions as the time variable t → 0 and t → +∞. By the Laplace transform method, we show that the solutions decay logarithmic...
متن کاملFractional chemotaxis diffusion equations.
We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modeling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macromolecular crowding. The mesoscopic models are formulated using continuous time random walk equations and the macroscopic models are formulated with fractiona...
متن کاملInhomogeneous Fractional Diffusion Equations
Fractional diffusion equations are abstract partial differential equations that involve fractional derivatives in space and time. They are useful to model anomalous diffusion, where a plume of particles spreads in a different manner than the classical diffusion equation predicts. An initial value problem involving a space-fractional diffusion equation is an abstract Cauchy problem, whose analyt...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Dynamics and Differential Equations
سال: 2022
ISSN: ['1040-7294', '1572-9222']
DOI: https://doi.org/10.1007/s10884-022-10224-4