Global well-posedness and exponential stability results of Bresse-Timoshenko system-type with second sound and distributed delay terms

Islah  Atmania; Salah Zitouni; Fatiha   Mesloub; Djamel   Ouchenane

doi:10.5269/bspm.63143

Islah Atmania Université de Larbi Tebessi
Salah Zitouni Department of Mathematics and Computer Science Souk Ahras . Algeria,
Fatiha Mesloub
Djamel Ouchenane

Resumo

In this paper, we investigate a Bresse-Timoshenko-type system with a distributed delay term and second sound. Under suitable assumptions, we establish the global well-posedness of the initial and boundary value problem by using the Faedo-Galerkin approximations and some energy estimates.

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Referências

H. Bahouri, J.-Y. Chemin, R. Danchin, Fourier Analysis and Nonlinear Partial Differential Equations, (Vol. 343, pp. 523-pages), Berlin: Springer, (2011).

P. Biler, G. Karch, Blowup of solutions to generalized Keller-Segel model, J. Evol. Equ. 10 (2010) 247262.

P. Biler, G. Wu, Two-dimensional chemotaxis models with fractional diffusion, Math. Methods Appl. Sci. 32, (2009) 112126.

J.M. Bony, Calcul symbolique et propagation des singularits pour les quations aux drives partielles non linaires, Ann. Sci. cole Norm. Sup. 14(4) (1981), 209246.

L. Caarelli, J. L. Vazquez, Nonlinear porous medium ow with fractional potential pressure, Arch Rational Mech Anal, 202(2011), 537-565.

M. Cannone, G. Wu, Global well-posedness for NavierStokes equations in critical FourierHerz spaces, Nonlinear Analysis: Theory, Methods and Applications, 75(9) (2012), 3754-3760.

L. Corrias, B. Perthame, H. Zaag, Global solutions of some chemotaxis and angiogenesis system in high space dimensions, Milan J. Math. 72 (2004), 128.

Y. Cui, W. Xiao, GEVREY REGULARITY AND TIME DECAY OF THE FRACTIONAL DEBYE-HCKEL SYSTEM IN FOURIER-BESOV SPACES, Bulletin of the Korean Mathematical Society, 57(6) (2020), 1393-1408.

C. Escudero, The fractional Keller-Segel model, Nonlinearity 19, (2006) 29092918.

T. Iwabuchi, Global well-posedness for KellerSegel system in Besov type spaces, J. Math. Anal. Appl. 379 (2) (2011), 930948.

E. F. Keller, L. A. Segel, Initiation of slime mold aggregation viewed as an instability, Journal of theoretical biology, 26(3)(1970), 399-415.

P. Konieczny, T. Yoneda, On dispersive eect of the Coriolis force for the stationary Navier-Stokes equations, J. Differ. Equ. 250 (2011), 3859-3873.

H. Kozono, Y. Sugiyama, Local existence and finite time blow-up of solutions in the 2-D KellerSegel system, J. Evol. Equ. 8 (2) (2008), 353378.

P.G. Lemari-Rieusset, Recent developments in the Navier-Stokes problem, Research Notes in Mathematics, Chapman and Hall/CRC, Boca Raton (2002).

P.-G. Lemari-Rieusset, Small data in an optimal Banach space for the parabolic-parabolic and parabolic-elliptic Keller- Segel equations in the whole space, Adv. Differ. Equ. 18 (2013), 11891208.

Z. Lei, F. Lin, Global mild solutions of Navier-Stokes equations, Commun. Pure Appl. Math. 64 (2011), 1297-1304.

T. Ogawa, S. Shimizu, The drift diffusion system in two-dimensional critical Hardy spaces, J. Funct. Anal., 255 (2008), 11071138.

T. Ogawa, S. Shimizu, End-point maximal regularity and its application to two-dimensional KellerSegel system, Math. Z. 264 (2010), 601628.

T. Ogawa, M. Yamamoto, Asymptotic behavior of solutions to drift-diffusion system with generalized dissipation, Mathematical Models and Methods in Applied Sciences, 19(06) (2009), 939-967.

S. Serfaty, J. L. Vazquez, A mean field equation as limit of nonlinear diffusions with fractional Laplacian operators, Calculus of Variations and Partial Differential Equations, 49(2014), 1091-1120.

M. Toumlilin, Global well-posedness and analyticity for generalized porous medium equation in critical Fourier-Besov- Morrey spaces, Open J. Math. Anal, 3(2019), 71-80.

W. Xiao, J. Chen, D. Fan, X. Zhou, Global Well-Posedness and Long Time Decay of Fractional Navier-Stokes Equations in Fourier Besov Spaces, In Abstract and Applied Analysis (Vol.2014), Hindawi Publishing Corporation.

W. Xiao, Y. Zhang, Gevrey Regularity and Time Decay of Fractional Porous Medium Equation in Critical Besov Spaces, Journal of Applied Mathematics and Physics, 10(1) (2022), 91-111.

W. Xiao, X. Zhou, On the Generalized Porous Medium Equation in Fourier-Besov Spaces, J. Math. Study., 53 (2020), 316-328.

Z. Zhai, Global well-posedness for nonlocal fractional Keller-Segel systems in critical Besov spaces, Nonlinear Anal. 72 (2010) 31733189.

J. Zhao, Well-posedness and Gevrey analyticity of the generalized KellerSegel system in critical Besov spaces, Annali di Matematica Pura ed Applicata (1923-), 197 (2018), 521-548.