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CONVOLUTION KERNEL IDENTIFICATION PROBLEM FOR MULTI-DIMENSIONAL TIME FRACTIONAL DIFFUSION-WAVE EQUATION IN BOUNDED DOMAIN
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AI
DOI：10.13108/2026-18-1-99.png)
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Abstract
En 中文
We study the inverse problem on determining the convolution kernel of integral term in an initial boundary value problem for a multi-dimensional time fractional diffusion-wave equation with the uniformly elliptic operator in a divergent form. Moreover, as an overdetermination condition, a single observation at the point x0 is an element of Omega of the diffusion-wave process serves, where Omega subset of R-n is a bounded domain. By the Fourier spectral method and fractional integro-differentiating technics the inverse problem is reduced to a convolution nonlinear Volterra integral equation of the second kind. The fixed point argument proves the local existence and global uniqueness results. Also the stability estimate for solution to inverse problem is obtained.
Keywords:
integro-differential equation
inverse problem
kernel
spectral problem
fixed point theorem
Gro & uml
nwall inequality
existence
uniqueness
Journal
U
IF:
0.4
Papers:
22
Citations:
0