.png){kind=icon}
.png){kind=icon}
Return
Stability estimates for nonlinear backward diffusion equations with superposition operators of mixed orders and time-dependent coefficients
.png){kind=icon}
PRE
AI
T
Q
DOI：10.1088/1361-6420/ae5087.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
This research paper delves into the inverse problem of reconstructing the historical distribution for a nonlinear diffusion equation, taking into account the superposition operator with mixed fractional orders and time-varying coefficients. The investigated problem, which broadens the scope of several earlier models, arises naturally from the superposition of multiple stochastic processes with different scales, including classical random walks and L & eacute;vy flights. Utilizing the Banach fixed point theorem alongside suitable estimates, we prove the ill-posedness of the problem in the sense of Hadamard. We further propose a new version of the Volterra integral equation method, along with the globally Lipschitz approximation technique to regularize the problem in both cases: globally and locally Lipschitz reaction terms. A conditional stability estimate for the solution of the backward problem is also obtained. In the end, a variety of numerical tests, utilizing a combination of finite difference schemes and the fast Fourier transform algorithm, are showcased to exemplify the theoretical results.
Keywords:
non-local diffusion equation
superposition operators of mixed order
ill-posed problem
integral equation method
Journal
I
IF:
2.1
Papers:
78
Citations:
8.4K
Organization
Cited Papers