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Eventual positivity and asymptotic behaviour for higher-order evolution equations. (Abstract of thesis). (English) Zbl 1542.47058

MSC:

47D06 One-parameter semigroups and linear evolution equations
35K25 Higher-order parabolic equations
46B42 Banach lattices
Full Text: DOI

References:

[1] Addona, D., Gregorio, F., Rhandi, A. and Tacelli, C., ‘Bi-Kolmogorov type operators and weighted Rellich’s inequalities’, Nonlinear Differ. Equ. Appl.29 (2022), Article no. 13, 37 pages. · Zbl 07474284
[2] Arora, S., ‘Locally eventually positive operator semigroups’, J. Operator Theory88(1) (2022), 203-242. · Zbl 07734181
[3] Bátkai, A., Kramar Fijavž, M. and Rhandi, A., Positive Operator Semigroups, Operator Theory: Advances and Applications, 257 (Birkhäuser/Springer, Cham, 2017). · Zbl 1420.47001
[4] Daners, D., ‘Non-positivity of the semigroup generated by the Dirichlet-to-Neumann operator’, Positivity18 (2014), 235-256. · Zbl 1375.35139
[5] Daners, D., Glück, J. and Kennedy, J. B., ‘Eventually positive semigroups of linear operators’, J. Math. Anal. Appl.433 (2016), 1561-1593. · Zbl 1339.47057
[6] Daners, D., Glück, J. and Kennedy, J. B., ‘Eventually and asymptotically positive semigroups on Banach lattices’, J. Differential Equations261 (2016), 2607-2649. · Zbl 1380.47036
[7] Daners, D., Glück, J. and Mui, J., ‘Local uniform convergence and eventual positivity of solutions to biharmonic heat equations’, Differential Integral Equations36(9/10) (2023), 727-756. · Zbl 1538.35189
[8] Denk, R., Kunze, M. and Ploß, D., ‘The bi-Laplacian with Wentzell boundary conditions on Lipschitz domains’, Integr. Equ. Oper. Theory93 (2021), Article no. 13, 26 pages. · Zbl 1462.35164
[9] Ferreira, L. C. F. and Ferreira, V. A. Jr., ‘On the eventual local positivity for polyharmonic heat equations’, Proc. Amer. Math. Soc.147 (2019), 4329-4341. · Zbl 1428.35154
[10] Ferrero, A., Gazzola, F. and Grunau, H.-C., ‘Decay and eventual local positivity for biharmonic parabolic equations’, Discrete Contin. Dyn. Syst.21 (2008), 1129-1157. · Zbl 1172.35029
[11] Gazzola, F. and Grunau, H.-C., ‘Eventual local positivity for a biharmonic heat equation in \({\mathbb{R}}^n\)’, Discrete Contin. Dyn. Syst. Ser. S1 (2008), 83-87. · Zbl 1153.35304
[12] Glück, J., ‘Evolution equations with eventually positive solutions’, Eur. Math. Soc. Magazine123 (2022), 4-11. · Zbl 1496.35030
[13] Gregorio, F. and Mugnolo, D., ‘Bi-Laplacians on graphs and networks’, J. Evol. Equ.20 (2020), 191-232. · Zbl 1437.35424
[14] Mui, J., ‘Spectral properties of locally eventually positive operator semigroups’, Semigroup Forum106 (2023), 460-480. · Zbl 1522.47067
[15] Noutsos, D. and Tsatsomeros, M. J., ‘Reachability and holdability of nonnegative states’, SIAM J. Matrix Anal. Appl.30 (2008), 700-712. · Zbl 1159.93004
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