Existence and regularity results of a backward problem for fractional diffusion equations
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DOI: 10.1002/mma.5781
Abstract: In this paper, we study a backward problem for an inhomogeneous fractional diffusion equation in a bounded domain. By applying the properties of Mittag‐Leffler functions and the method of eigenvalue expansion, we establish some results… read more here.
Keywords: fractional diffusion; problem; existence regularity; backward problem ... See more keywords
Regularization of a backward problem for the inhomogeneous time‐fractional wave equation
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DOI: 10.1002/mma.6285
Abstract: In this paper, we consider a backward problem for an inhomogeneous time‐fractional wave equation in a general bounded domain. Such a backward problem is of practically great importance because we often do not know the… read more here.
Keywords: inhomogeneous time; problem; time fractional; problem inhomogeneous ... See more keywords
A backward problem for distributed order diffusion equation: uniqueness and numerical solution
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DOI: 10.1080/17415977.2020.1795152
Abstract: In this paper we consider the identification of the initial condition for a distributed order diffusion equation. We first prove the unique existence and the regularity properties of the strong solution on the bounded temporal-spacial… read more here.
Keywords: order diffusion; distributed order; backward problem; diffusion equation ... See more keywords
Stability and numerical analysis of backward problem for subdiffusion with time-dependent coefficients
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DOI: 10.1088/1361-6420/acb007
Abstract: Our aim is to study the backward problem, i.e. recover the initial data from the terminal observation, of the subdiffusion with time dependent coefficients. First of all, by using the smoothing property of solution operators… read more here.
Keywords: problem; time; time dependent; dependent coefficients ... See more keywords
Galerkin Method for a Backward Problem of Time-Space Fractional Symmetric Diffusion Equation
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DOI: 10.3390/sym15051057
Abstract: We investigate a backward problem of the time-space fractional symmetric diffusion equation with a source term, wherein the negative Laplace operator −Δ contained in the main equation belongs to the category of uniformly symmetric elliptic… read more here.
Keywords: problem; time space; equation; space fractional ... See more keywords