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Carvalho-Neto, Paulo Mendes de; Planas, Gabriela

doi:10.1016/j.jde.2015.04.008

Cited by 143 publications

(118 citation statements)

References 30 publications

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“…Let u be a classical solution to (16). Then, there exists a (nonnegative) classical solution ρ to (17). Moreover, we have the estimate…”

Section: Gradient Boundmentioning

confidence: 91%

“…Step 1. Existence and uniqueness of solutions to (17). It follows by the result of [32,Section 5] (see also [46,Section 2]).…”

Section: Gradient Boundmentioning

confidence: 91%

“…denotes the Mainardi function (see [49]). We recall the following useful property of M β (see [17,Proposition 2]). Note that E β (−t β A) and E β,β (−t β A) are well-defined from X into X and, for every x ∈ X, the functions t −→ E β (−t β A)x and t −→ E β,β (−t β A)x are analytic from [0, ∞) to X.…”

Section: On Time-fractional Heat Equations: L P -Maximal Regularity Rmentioning

confidence: 99%

“…We test (23) against the adjoint variable ρ solving (17). Using Lemma 5.2 and integrating by parts in space we get…”

Section: Gradient Boundmentioning

confidence: 99%

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Existence and regularity results for viscous Hamilton–Jacobi equations with Caputo time-fractional derivative

Camilli

Goffi

2020

Nonlinear Differ. Equ. Appl.

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“…Let u be a classical solution to (16). Then, there exists a (nonnegative) classical solution ρ to (17). Moreover, we have the estimate…”

Section: Gradient Boundmentioning

confidence: 91%

“…Step 1. Existence and uniqueness of solutions to (17). It follows by the result of [32,Section 5] (see also [46,Section 2]).…”

Section: Gradient Boundmentioning

confidence: 91%

Section: On Time-fractional Heat Equations: L P -Maximal Regularity Rmentioning

confidence: 99%

“…We test (23) against the adjoint variable ρ solving (17). Using Lemma 5.2 and integrating by parts in space we get…”

Section: Gradient Boundmentioning

confidence: 99%

See 2 more Smart Citations

Existence and regularity results for viscous Hamilton–Jacobi equations with Caputo time-fractional derivative

Camilli

Goffi

2020

Nonlinear Differ. Equ. Appl.

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“…In this section, we present the definitions of -stable Levy noise, fractional operators, special functions, and the mild solutions for stochastic system (1), which are from previous studies. [5][6][7]15 Definition 2.1. A stochastic process L t is called as -stable Levy motion with 0 < ≤ 2 if…”

Section: Notations and Preliminariesmentioning

confidence: 99%

Well‐posedness of time‐space fractional stochastic evolution equations driven by α‐stable noise

Huang

Zou

2019

Math Methods in App Sciences

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This paper is devoted to the well‐posedness for time‐space fractional Ginzburg‐Landau equation and time‐space fractional Navier‐Stokes equations by α‐stable noise. The spatial regularity and the temporal regularity of the nonlocal stochastic convolution are firstly established, and then the existence and uniqueness of the global mild solution are obtained by the Banach fixed point theorem and Mittag‐Leffler functions, respectively. Numerical simulations for time‐space fractional Ginzburg‐Landau equation are provided to verify the analysis results.

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Existence and asymptotic behaviour for the time‐fractional Keller–Segel model for chemotaxis

Azevedo

Cuevas

Henriquez

2018

Mathematische Nachrichten

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One of the most important systems for understanding chemotactic aggregation is the Keller-Segel system. We consider the time-fractional Keller-Segel system of order ∈ (0, 1). We prove an existence result with small initial data in a class of Besov-Morrey spaces. Self-similar solutions are obtained and we also show an asymptotic behaviour result. K E Y W O R D SBesov-Morrey, chemotaxis aggregation, fractional derivative, Keller-Segel model, spaces M S C ( 2 0 1 0 ) 26A33, 35A01, 35B40, 35K45, 35K55, 35Q92, 35R11, 92C15, 92C17

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Mild solutions to the time fractional Navier–Stokes equations inRN

Cited by 143 publications

References 30 publications

Existence and regularity results for viscous Hamilton–Jacobi equations with Caputo time-fractional derivative

Existence and regularity results for viscous Hamilton–Jacobi equations with Caputo time-fractional derivative

Well‐posedness of time‐space fractional stochastic evolution equations driven by α‐stable noise

Existence and asymptotic behaviour for the time‐fractional Keller–Segel model for chemotaxis

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