RUS  ENG
Full version
JOURNALS // Matematicheskie Zametki

Mat. Zametki, 2020, Volume 108, Issue 6, Pages 911–919 (Mi mzm12931)

Nonexistence of Global Weak Solutions for Evolution Equations with Fractional Laplacian
A. Z. Fino, E. I. Galakhov, O. A. Salieva

References

1. Q. S. Zhang, “A blow up result for a nonlinear wave equation with damping: the critical case”, C. R. Acad. Sci. Paris Sér. I Math., 333:2 (2001), 109–114  crossref  mathscinet  zmath
2. E. Mitidieri, S. I. Pokhozhaev, “Apriornye otsenki i otsutstvie reshenii nelineinykh uravnenii i neravenstv v chastnykh proizvodnykh”, Tr. MIAN, 234, Nauka, MAIK «Nauka/Interperiodika», M., 2001, 3–383  mathnet  mathscinet  zmath
3. S. I. Pokhozhaev, “Suschestvenno nelineinye emkosti, indutsirovannye differentsialnymi operatorami”, Dokl. AN, 56 (1997), 924–926  mathscinet  zmath
4. A. Z. Fino, M. Kirane, “Qualitative properties of solutions to a time-space fractional evolution equation”, Quart. Appl. Math., 70 (2012), 133–157  crossref  mathscinet  zmath
5. M. Gidda, M. Kirane, “Kritichnost dlya nekotorykh evolyutsionnykh uravnenii”, Differents. uravneniya, 37:4 (2001), 511–520  mathnet  mathscinet
6. M. Kirane, Y. Laskri, N.-E. Tatar, “Critical exponents of Fujita type for certain evolution equations and systems with spatio-temporal fractional derivatives”, J. Math. Anal. Appl., 312:2 (2005), 488–501  crossref  mathscinet  zmath
7. P. Baras, R. Kersner, “Local and global solvability of a class of semilinear parabolic equations”, J. Differential Equations, 68:2 (1987), 238–252  crossref  mathscinet  zmath
8. A. Carbotti, S. Dipierro, E. Valdinoci, Local Density of Solutions of Time and Space Fractional Equations, 2018, arXiv: 1810.08448
9. S. Dipierro, H.-C. Grunau, “Boggio's formula for fractional polyharmonic Dirichlet problems”, Ann. Mat. Pura Appl. (4), 196:4 (2017), 1327–1344  crossref  mathscinet  zmath
10. S. Dipierro, O. Savin, E. Valdinoci, “All functions are locally s-harmonic up to a small error”, J. Eur. Math. Soc. (JEMS), 19:4 (2017), 957–966  crossref  mathscinet  zmath
11. N. V. Krylov, On the Paper "All Functions are Locally $s$-Harmonic up to a Small Error" by Dipierro, Savin, and Valdinoci, 2018, arXiv: 1810.07648
12. Z. Dahmani, F. Karami, S. Kerbal, “Nonexistence of positive solutions to nonlinear nonlocal elliptic systems”, J. Math. Anal. Appl., 346:1 (2008), 22–29  crossref  mathscinet  zmath
13. E. Galakhov, O. Salieva, “Nonexistence of solutions of some inequalities with gradient nonlinearities and fractional Laplacian”, Proceedings of EQUADIFF 2017, SPEKTRUM STU Publishing, Bratislava, 2017, 157–162
14. E. I. Galakhov, O. A. Salieva, “Uniqueness of the trivial solution of some inequalities with fractional Laplacian”, Electron. J. Qual. Theory Differ. Equ., 2019:1 (2019), 1–8  crossref  mathscinet  zmath
15. O. A. Salieva, “Otsutstvie reshenii nekotorykh nelineinykh neravenstv s drobnymi stepenyami operatora Laplasa”, Matem. zametki, 101:4 (2017), 588–593  mathnet  crossref  mathscinet  zmath
16. T. A. Dao, M. Reissig, A Blow-Up Result for Semi-Linear Structurally Damped $\sigma$-Evolution Equations, 2019, arXiv: 1909.01181v1
17. N. Ju, “The maximum principle and the global attractor for the dissipative 2D quasi-geostrophic equations”, Comm. Math. Phys., 255:1 (2005), 161–181  mathscinet  zmath
18. K. Bogdan, T. Byczkowski, “Potential theory for the $\alpha$-stable Schrödinger operator on bounded Lipschitz domains”, Studia Math., 133:1 (1999), 53–92  crossref  mathscinet  zmath


© Steklov Math. Inst. of RAS, 2026