Global Unsolvability of the Burgers Equation with Fractional Time Derivative

Torebek, Berikbol T.

doi:10.1134/s0012266119060156

Cited by 6 publications

(5 citation statements)

References 6 publications

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“…We also note that the results of local existence and blow-up of solutions for the (time, space, time-space) fractional analogues of diffusion equations with different non-linearities (power nonlinearities, combined nonlinearities, nonlocal nonlinearities and other nonlinearities) have been studied by many authors (see for example [7,11,18,20,21] and references therein). Let us briefly recall some definitions of the Riemann-Liouville integral, fractional Riemann-Liouville, and Caputo derivatives.…”

Section: Results On R Nmentioning

confidence: 99%

Sub-diffusion equations with Mittag-Leffler nonlinearity

Torebek

2023

DCDS-S

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<p style='text-indent:20px;'>The paper is devoted to the study of subdiffusion equations with Mittag-Leffler nonlinearity. The comparison principle is proved in a bounded domain. The results on the local existence, global existence, and blow-up of solutions to the initial-boundary value problem are obtained. In addition, the results of local existence and blow-up of solutions to the initial problem on the whole Euclidean space are proven.</p>

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Section: Results On R Nmentioning

confidence: 99%

Sub-diffusion equations with Mittag-Leffler nonlinearity

Torebek

2023

DCDS-S

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“…then (1.5) admits no weak solution. For other works related to nonexistence results for time-fractionally evolution equations, see e.g., [27][28][29][30][31][32][33][34][35] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

On a one-dimensional time-fractionally damped wave equation with a singular potential

Jleli,

Samet

2024

Phys. Scr.

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A nonlinear time-fractionally damped wave equation with an inverse-square potential posed on the interval (0, 1) is investigated. The time-fractionally derivative is considered in the Caputo sense. A weight function of the form x −σ ( σ ∈ R ) is allowed in front of the nonlinearity ∣u(t, x)∣ p (p > 1). The problem is studied under certain initial conditions and a homogeneous boundary condition. Namely, we obtain sufficient conditions under which the considered problem admits no weak solution. The cases u(0, · ) ≡ 0 and u(0, · ) ≢ 0 are studied separately.

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“…Next, they discussed the influence of gradient nonlinearity on the global solvability of (3) under certain boundary conditions. Problem (3) was also investigated in [14] by Torebek, where he obtained sufficient conditions depending on the initial value u(0, •) and the boundary conditions, for which there does not exist a global solution to (3).…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, motivated by [10,14], we first consider the fractional-in-space analogue of (1) on a bounded interval, namely,…”

Section: Introductionmentioning

confidence: 99%

Blow-Up of Solutions to Fractional-in-Space Burgers-Type Equations

2021

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We consider fractional-in-space analogues of Burgers equation and Korteweg-de Vries-Burgers equation on bounded domains. Namely, we establish sufficient conditions for finite-time blow-up of solutions to the mentioned equations. The obtained conditions depend on the initial value and the boundary conditions. Some examples are provided to illustrate our obtained results. In the proofs of our main results, we make use of the test function method and some integral inequalities.

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Global Unsolvability of the Burgers Equation with Fractional Time Derivative

Cited by 6 publications

References 6 publications

Sub-diffusion equations with Mittag-Leffler nonlinearity

Sub-diffusion equations with Mittag-Leffler nonlinearity

On a one-dimensional time-fractionally damped wave equation with a singular potential

Blow-Up of Solutions to Fractional-in-Space Burgers-Type Equations

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