Global existence and blowup of solutions to semilinear fractional reaction-diffusion equation with singular potential

Tan, Zhong; Xie, Minghong

doi:10.1016/j.jmaa.2020.124548

Cited by 6 publications

(3 citation statements)

References 17 publications

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“…Due to unprecedented modeling capability of the model (1.1), the analytical study of the direct problem of (1.1) has received much more attention in recent years. For well-posedness, we refer to [3,32,37] and the references therein; for numerical methods, there are also some important literatures (see [19,24] and the references therein).…”

Section: (T)(u(t) ϕ) = (A(t)∇u(t) + B(t)u(t) ∇ϕ)mentioning

confidence: 99%

Inverse potential problem for a semilinear generalized fractional diffusion equation with spatio-temporal dependent coefficients

Ma¹,

Sun²

2022

Inverse Problems

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In this work, we are interested in an inverse potential problem for a semilinear generalized fractional diﬀusion equation with a time-dependent principal part. The missing time-dependent potential is reconstructed from an additional integral measured data over the domain. Due to the nonlinearity of the equation and arising of a space-time dependent principal part operator in the model, such a nonlinear inverse problem is novel and signiﬁcant. The well-posedness of the forward problem is ﬁrstly investigated by using the well known Rothe’s method. Then the existence and uniqueness of the inverse problem are obtained by employing the Arzel`a-Ascoli theorem, a coerciveness of the fractional derivative and Gronwall’s inequality, as well as the regularities of the direct problem. Also, the ill-posedness of the inverse problem is proved by analyzing the properties of the forward operator. Finally a modiﬁed non-stationary iterative Tikhonov regularization method is used to ﬁnd a stable approximate solution for the potential term. Numerical examples in one- and two-dimensional cases are provided to illustrate the eﬃciency and robustness of the proposed algorithm.

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Section: (T)(u(t) ϕ) = (A(t)∇u(t) + B(t)u(t) ∇ϕ)mentioning

confidence: 99%

Inverse potential problem for a semilinear generalized fractional diffusion equation with spatio-temporal dependent coefficients

Ma¹,

Sun²

2022

Inverse Problems

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“…Various extensions of (1.1) then follow. For examples, one may confer [14] for an investigation of (1.1) in the porous medium setting, [7] for the existence of global or finite time blow-up weak solutions of (1.1) when the initial energy is critical and most recently [12] for a fractional Laplace operator consideration.…”

Section: Introductionmentioning

confidence: 99%

On a Higher-order Reaction-diffusion Equation with a Special Medium Void via Potential Well Method

Duc

Trong

Thanh³

2023

Taiwanese J. Math.

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“…Besides the aforementioned papers, one may also confer [7,Section 14], [3][4][5][6]11] and the references therein for further investigations into higher-order parabolic problems in the literature. While for reaction-diffusion equations with special diffusion processes (or interchangeably, special medium voids) the papers [15,16] and their references therein are recommended.…”

Section: Introductionmentioning

confidence: 99%

Blow-up estimates for a higher-order reaction–diffusion equation with a special diffusion process

Thanh

Trong

Duc

2021

J Elliptic Parabol Equ

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Global existence and blowup of solutions to semilinear fractional reaction-diffusion equation with singular potential

Cited by 6 publications

References 17 publications

Inverse potential problem for a semilinear generalized fractional diffusion equation with spatio-temporal dependent coefficients

Inverse potential problem for a semilinear generalized fractional diffusion equation with spatio-temporal dependent coefficients

On a Higher-order Reaction-diffusion Equation with a Special Medium Void via Potential Well Method

Blow-up estimates for a higher-order reaction–diffusion equation with a special diffusion process

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