Duong, Giao Ky; Ghoul, Tej-Eddine; Zaag, Hatem Gradient blowup profile for the semilinear heat equation. (English) Zbl 1536.35099 Discrete Contin. Dyn. Syst. 44, No. 4, 997-1025 (2024). MSC: 35B44 35B40 35K15 35K58 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Casal, Alfonso Carlos; Díaz, Gregorio; Díaz, Jesús Ildefonso; Vegas, José Manuel Controlled boundary explosions: dynamics after blow-up for some semilinear problems with global controls. (English) Zbl 1518.35139 Discrete Contin. Dyn. Syst. 43, No. 3-4, 1201-1238 (2023). MSC: 35B44 35B60 35J66 35K58 49J30 34K40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Duong, Giao Ky; Nouaili, Nejla; Zaag, Hatem Construction of blowup solutions for the complex Ginzburg-Landau equation with critical parameters. (English) Zbl 1518.35001 Memoirs of the American Mathematical Society 1411. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-6121-8/pbk; 978-1-4704-7481-2/ebook). v, 91 p. (2023). MSC: 35-02 35B44 35K57 35Q56 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Abdelhedi, Bouthaina; Zaag, Hatem Single point blow-up and final profile for a perturbed nonlinear heat equation with a gradient and a non-local term. (English) Zbl 1479.35136 Discrete Contin. Dyn. Syst., Ser. S 14, No. 8, 2607-2623 (2021). MSC: 35B44 35K15 35K58 35R09 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Duong, G. K.; Kavallaris, N. I.; Zaag, H. Diffusion-induced blowup solutions for the shadow limit model of a singular Gierer-Meinhardt system. (English) Zbl 1477.35043 Math. Models Methods Appl. Sci. 31, No. 7, 1469-1503 (2021). MSC: 35B44 35B40 35K20 35K58 35R09 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fujishima, Yohei; Ishige, Kazuhiro Blowing up solutions for nonlinear parabolic systems with unequal elliptic operators. (English) Zbl 1445.35083 J. Dyn. Differ. Equations 32, No. 3, 1219-1231 (2020). MSC: 35B44 35K51 35K58 35R45 × Cite Format Result Cite Review PDF Full Text: DOI
Del Pino, Manuel; Musso, Monica; Wei, Juncheng; Zhou, Yifu Type II finite time blow-up for the energy critical heat equation in \(\mathbb{R}^4\). (English) Zbl 1439.35284 Discrete Contin. Dyn. Syst. 40, No. 6, 3327-3355 (2020). MSC: 35K58 35B40 × Cite Format Result Cite Review PDF Full Text: DOI
Wang, Chunhua; Wei, Juncheng; Wei, Suting; Zhou, Yifu Infinite time blow-up for critical heat equation with drift terms. (English) Zbl 1427.35134 Calc. Var. Partial Differ. Equ. 59, No. 1, Paper No. 3, 43 p. (2020). MSC: 35K58 35K55 35B40 × Cite Format Result Cite Review PDF Full Text: DOI
Ghoul, Tej-Eddine; Nguyen, Van Tien; Zaag, Hatem Construction of type I blowup solutions for a higher order semilinear parabolic equation. (English) Zbl 1416.35141 Adv. Nonlinear Anal. 9, 388-412 (2020). MSC: 35K58 35B40 35K55 35K57 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Duong, Giao Ky A blowup solution of a complex semi-linear heat equation with an irrational power. (English) Zbl 1428.35143 J. Differ. Equations 267, No. 9, 4975-5048 (2019). MSC: 35K05 35B40 35B44 35K55 35K57 35B09 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Duong, Giao Ky; Zaag, Hatem Profile of a touch-down solution to a nonlocal MEMS model. (English) Zbl 1425.35116 Math. Models Methods Appl. Sci. 29, No. 7, 1279-1348 (2019). MSC: 35K91 35B40 35K20 35K57 35B44 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Duong, Giao Ky Profile for the imaginary part of a blowup solution for a complex-valued semilinear heat equation. (English) Zbl 1417.35064 J. Funct. Anal. 277, No. 5, 1531-1579 (2019). MSC: 35K55 35K57 35B44 35B40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hamza, Mohamed Ali; Zaag, Hatem Prescribing the center of mass of a multi-soliton solution for a perturbed semilinear wave equation. (English) Zbl 1437.35500 J. Differ. Equations 267, No. 6, 3524-3560 (2019). MSC: 35L71 35L67 35L15 35B44 35B40 35B20 35C08 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Tayachi, Slim; Zaag, Hatem Existence of a stable blow-up profile for the nonlinear heat equation with a critical power nonlinear gradient term. (English) Zbl 1423.35186 Trans. Am. Math. Soc. 371, No. 8, 5899-5972 (2019). Reviewer: Johannes Lankeit (Paderborn) MSC: 35K55 35B44 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Duong, Giao Ky; Nguyen, Van Tien; Zaag, Hatem Construction of a stable blowup solution with a prescribed behavior for a non-scaling-invariant semilinear heat equation. (English) Zbl 1407.35092 Tunis. J. Math. 1, No. 1, 13-45 (2019). MSC: 35K05 35B40 35K55 35K57 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ghoul, Tej-Eddine; Nguyen, Van Tien; Zaag, Hatem Construction and stability of blowup solutions for a non-variational semilinear parabolic system. (Construction et stabilité de solutions explosives pour un système parabolique sémilinéaire non-variationel.) (English. French summary) Zbl 1394.35222 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 35, No. 6, 1577-1630 (2018). MSC: 35K45 35B44 35B40 35K55 35K57 35B35 35K91 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Merle, Frank; Zaag, Hatem Blowup solutions to the semilinear wave equation with a stylized pyramid as a blowup surface. (English) Zbl 1402.35181 Commun. Pure Appl. Math. 71, No. 9, 1850-1937 (2018). Reviewer: Dongbing Zha (Shanghai) MSC: 35L71 35B44 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Combet, Vianney; Martel, Yvan Construction of multibubble solutions for the critical gKdV equation. (English) Zbl 1397.35249 SIAM J. Math. Anal. 50, No. 4, 3715-3790 (2018). Reviewer: Piotr Biler (Wrocław) MSC: 35Q53 35B44 35B40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Nouaili, Nejla; Zaag, Hatem Construction of a blow-up solution for the complex Ginzburg-Landau equation in a critical case. (English) Zbl 1397.35295 Arch. Ration. Mech. Anal. 228, No. 3, 995-1058 (2018). Reviewer: Ayman Kachmar (Nabaṭiyya) MSC: 35Q56 35B44 35B35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ghoul, Tej-Eddine; Nguyen, Van Tien; Zaag, Hatem Blowup solutions for a reaction-diffusion system with exponential nonlinearities. (English) Zbl 1393.35096 J. Differ. Equations 264, No. 12, 7523-7579 (2018). Reviewer: Denise Huet (Nancy) MSC: 35K57 35B40 35K55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gustafson, Stephen; Roxanas, Dimitrios Global, decaying solutions of a focusing energy-critical heat equation in \(\mathbb{R}^4\). (English) Zbl 1391.35173 J. Differ. Equations 264, No. 9, 5894-5927 (2018). Reviewer: Dian K. Palagachev (Bari) MSC: 35K05 35B40 35B65 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Merle, Frank; Zaag, Hatem Solution to the semilinear wave equation with a pyramid-shaped blow-up surface. (English) Zbl 1475.35209 Sémin. Laurent Schwartz, EDP Appl. 2016-2017, Exp. No. 6, 13 p. (2017). MSC: 35L71 35B40 35B44 35C08 35L15 35L05 35L67 × Cite Format Result Cite Review PDF Full Text: DOI Numdam
Fan, Chenjie \(\log\)-\(\log\) blow up solutions blow up at exactly \(m\) points. (English. French summary) Zbl 1382.35263 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 34, No. 6, 1429-1482 (2017). Reviewer: Guido Schneider (Stuttgart) MSC: 35Q55 35B44 35B65 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fujishima, Yohei; Ishige, Kazuhiro; Maekawa, Hiroki Blow-up set of type I blowing up solutions for nonlinear parabolic systems. (English) Zbl 1377.35035 Math. Ann. 369, No. 3-4, 1491-1525 (2017). MSC: 35B44 35K40 35R45 × Cite Format Result Cite Review PDF Full Text: DOI
Lan, Yang Blow-up solutions for \(L^2\) supercritical gKdV equations with exactly \(k\) blow-up points. (English) Zbl 1373.35275 Nonlinearity 30, No. 8, 3203-3240 (2017). MSC: 35Q53 35B40 35B44 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ghoul, Tej-Eddine; Nguyen, Van Tien; Zaag, Hatem Blowup solutions for a nonlinear heat equation involving a critical power nonlinear gradient term. (English) Zbl 1378.35173 J. Differ. Equations 263, No. 8, 4517-4564 (2017). MSC: 35K58 35K55 35B40 35B44 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Mahmoudi, Fethi; Nouaili, Nejla; Zaag, Hatem Construction of a stable periodic solution to a semilinear heat equation with a prescribed profile. (English) Zbl 1334.35145 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 131, 300-324 (2016). Reviewer: Hussein Fakih (Poitiers) MSC: 35K58 35B44 35B35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Nouaili, Nejla; Zaag, Hatem Profile for a simultaneously blowing up solution to a complex valued semilinear heat equation. (English) Zbl 1335.35126 Commun. Partial Differ. Equations 40, No. 7, 1197-1217 (2015). Reviewer: Christian Stinner (Kaiserslautern) MSC: 35K57 35K40 35B44 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ru, S.; Chen, Jiecheng The blow-up solutions of the heat equations in \(\mathcal{F} L^1(\mathbb R^N)\). (English) Zbl 1323.35054 J. Funct. Anal. 269, No. 5, 1264-1288 (2015). Reviewer: Dian K. Palagachev (Bari) MSC: 35K05 35K55 × Cite Format Result Cite Review PDF Full Text: DOI
Fujishima, Yohei; Ishige, Kazuhiro Blow-up set for type I blowing up solutions for a semilinear heat equation. (English) Zbl 1297.35052 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 31, No. 2, 231-247 (2014). MSC: 35B44 35K58 35K20 × Cite Format Result Cite Review PDF Full Text: DOI
Hirata, Kentaro Removable singularities of semilinear parabolic equations. (English) Zbl 1278.35007 Proc. Am. Math. Soc. 142, No. 1, 157-171 (2014). Reviewer: Marius Ghergu (Dublin) MSC: 35A20 35B65 35K91 35K58 35B44 × Cite Format Result Cite Review PDF Full Text: DOI
Pak, Hee Chul Blow-up time for nonlinear heat equations with transcendental nonlinearity. (English) Zbl 1257.35054 J. Appl. Math. 2012, Article ID 202137, 8 p. (2012). MSC: 35B44 35K58 × Cite Format Result Cite Review PDF Full Text: DOI
Fujishima, Yohei; Ishige, Kazuhiro Blow-up for a semilinear parabolic equation with large diffusion on \(\mathbf R^N\). II. (English) Zbl 1255.35055 J. Differ. Equations 252, No. 2, 1835-1861 (2012). Reviewer: Marek Fila (Bratislava) MSC: 35B44 35K58 × Cite Format Result Cite Review PDF Full Text: DOI
Fujishima, Yohei; Ishige, Kazuhiro Blow-up for a semilinear parabolic equation with large diffusion on \(\mathbb R^N\). (English) Zbl 1225.35034 J. Differ. Equations 250, No. 5, 2508-2543 (2011). Reviewer: Marek Fila (Bratislava) MSC: 35B44 35K91 × Cite Format Result Cite Review PDF Full Text: DOI
Khenissy, S.; Rébaï, Y.; Zaag, H. Continuity of the blow-up profile with respect to initial data and to the blow-up point for a semilinear heat equation. (English) Zbl 1215.35090 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 28, No. 1, 1-26 (2011). MSC: 35K58 35B44 35B30 × Cite Format Result Cite Review PDF Full Text: DOI
Fujishima, Yohei; Ishige, Kazuhiro Blow-up set for a semilinear heat equation with small diffusion. (English) Zbl 1204.35054 J. Differ. Equations 249, No. 5, 1056-1077 (2010). Reviewer: Marek Fila (Bratislava) MSC: 35B44 35K57 35B40 35K58 35K15 35B09 × Cite Format Result Cite Review PDF Full Text: DOI
Bonder, Julian Fernández; Groisman, Pablo; Rossi, Julio D. Continuity of the explosion time in stochastic differential equations. (English) Zbl 1175.60057 Stochastic Anal. Appl. 27, No. 5, 984-999 (2009). MSC: 60H10 34F05 × Cite Format Result Cite Review PDF Full Text: DOI
Dejak, Steven; Gang, Zhou; Sigal, Israel Michael; Wang, Shuangcai Blow-up in nonlinear heat equations. (English) Zbl 1180.35130 Adv. Appl. Math. 40, No. 4, 433-481 (2008). Reviewer: Jiaqi Mo (Wuhu) MSC: 35B44 35K57 35K55 35K15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Masmoudi, Nader; Zaag, Hatem Blow-up profile for the complex Ginzburg-Landau equation. (English) Zbl 1158.35016 J. Funct. Anal. 255, No. 7, 1613-1666 (2008). Reviewer: Vicenţiu D. Rădulescu (Craiova) MSC: 35B40 35K55 35Q55 × Cite Format Result Cite Review PDF Full Text: DOI
Pérez-Llanos, Mayte; Rossi, Julio D. Nontrivial compact blow-up sets of smaller dimension. (English) Zbl 1132.35014 Proc. Am. Math. Soc. 136, No. 2, 593-596 (2008). Reviewer: Peter Lindqvist (Trondheim) MSC: 35B40 35K65 × Cite Format Result Cite Review PDF Full Text: DOI
Fiedler, Bernold; Matano, Hiroshi Global dynamics of blow-up profiles in one-dimensional reaction diffusion equations. (English) Zbl 1132.35048 J. Dyn. Differ. Equations 19, No. 4, 867-893 (2007). Reviewer: Messoud A. Efendiev (Berlin) MSC: 35K57 35B40 42A15 × Cite Format Result Cite Review PDF Full Text: DOI
Cortazar, Carmen; Elgueta, Manuel; Rossi, Julio D. The blow-up problem for a semilinear parabolic equation with a potential. (English) Zbl 1131.35039 J. Math. Anal. Appl. 335, No. 1, 418-427 (2007). Reviewer: Peter Poláčik (Minneapolis) MSC: 35K55 35K57 35K20 35B05 35K15 35B40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dickstein, Flávio Blowup stability of solutions of the nonlinear heat equation with a large life span. (English) Zbl 1100.35044 J. Differ. Equations 223, No. 2, 303-328 (2006). Reviewer: Marek Fila (Bratislava) MSC: 35K55 35K57 35B40 35K15 × Cite Format Result Cite Review PDF Full Text: DOI
Ishige, Kazuhiro; Yagisita, Hiroki Blow-up problems for a semilinear heat equation with large diffusion. (English) Zbl 1072.35096 J. Differ. Equations 212, No. 1, 114-128 (2005). Reviewer: Hanna Marcinkowska (Wrocław) MSC: 35K60 35K55 35B05 35B33 × Cite Format Result Cite Review PDF Full Text: DOI
Groisman, Pablo; Rossi, Julio D.; Zaag, Hatem On the dependence of the blow-up time with respect to the initial data in a semilinear parabolic problem. (English) Zbl 1036.35025 Commun. Partial Differ. Equations 28, No. 3-4, 737-744 (2003). Reviewer: Marek Fila (Bratislava) MSC: 35B30 35K15 35K20 35K55 35B40 × Cite Format Result Cite Review PDF Full Text: DOI
Zaag, Hatem On the regularity of the blow-up set for semilinear heat equations. (English) Zbl 1012.35039 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 19, No. 5, 505-542 (2002). Reviewer: A.Cichocka (Katowice) MSC: 35K55 35K15 35K05 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML
Groisman, Pablo; Rossi, Julio D. Asymptotic behaviour for a numerical approximation of a parablic problem with blowing up solutions. (English) Zbl 0991.65090 J. Comput. Appl. Math. 135, No. 1, 135-155 (2001). Reviewer: Dana Petcu (Timişoara) MSC: 65M20 65M12 35K55 35B40 × Cite Format Result Cite Review PDF Full Text: DOI
Ushijima, Takeo K. On the approximation of blow-up time for solutions of nonlinear parabolic equations. (English) Zbl 0981.65106 Publ. Res. Inst. Math. Sci. 36, No. 5, 613-640 (2000). Reviewer: H.Marcinkowska (Wrocław) MSC: 65M12 35K55 65M20 × Cite Format Result Cite Review PDF Full Text: DOI
Zaag, Hatem A remark on the energy blow-up behavior for nonlinear heat equations. (English) Zbl 0971.35042 Duke Math. J. 103, No. 3, 545-556 (2000). Reviewer: A.Cichocka (Katowice) MSC: 35K60 35K20 35K55 35A20 35B40 35B05 × Cite Format Result Cite Review PDF Full Text: DOI
Mizoguchi, Noriko; Yanagida, Eiji Critical exponents for the blowup of solutions with sign changes in a semilinear parabolic equation. II. (English) Zbl 0924.35055 J. Differ. Equations 145, No. 2, 295-331 (1998). Reviewer: C.Y.Chan (Lafayette) MSC: 35K15 35B40 35K57 × Cite Format Result Cite Review PDF Full Text: DOI
Zaag, Hatem Blow-up results for vector-valued nonlinear heat equations with no gradient structure. (English) Zbl 0902.35050 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 15, No. 5, 581-622 (1998). Reviewer: Dian Palagachev (Sofia) MSC: 35K40 35B40 35K50 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML
Mizoguchi, Noriko; Ninomiya, Hirokazu; Yanagida, Eiji Critical exponent for the bipolar blowup in a semilinear parabolic equation. (English) Zbl 0914.35064 J. Math. Anal. Appl. 218, No. 2, 495-518 (1998). Reviewer: M.A.Vivaldi (Roma) MSC: 35K60 35B40 × Cite Format Result Cite Review PDF Full Text: DOI
Merle, Frank; Zaag, Hatem Stability of the blow-up profile for equations of the type \(u_ t=\Delta u+| u| ^{p-1}u\). (English) Zbl 0872.35049 Duke Math. J. 86, No. 1, 143-195 (1997). Reviewer: D.Palagachev (Sofia) MSC: 35K55 35B40 35K15 × Cite Format Result Cite Review PDF Full Text: DOI
Filippas, Stathis; Merle, Frank Compactness and single-point blowup of positive solutions on bounded domains. (English) Zbl 0874.35053 Proc. R. Soc. Edinb., Sect. A 127, No. 1, 47-65 (1997). Reviewer: C.Y.Chan (Lafayette) MSC: 35K60 35B40 35K57 × Cite Format Result Cite Review PDF Full Text: DOI
Chen, Chao-Nien Infinite time blow-up of solutions to a nonlinear parabolic problem. (English) Zbl 0887.35079 J. Differ. Equations 139, No. 2, 409-427 (1997). MSC: 35K60 35B40 35B05 × Cite Format Result Cite Review PDF Full Text: DOI
Etheridge, Alison M. A probabilistic approach to blow-up of a semilinear heat equation. (English) Zbl 0876.60071 Proc. R. Soc. Edinb., Sect. A 126, No. 6, 1235-1245 (1996). Reviewer: A.D.Borisenko (Kiev) MSC: 60J80 60H15 35K99 × Cite Format Result Cite Review PDF Full Text: DOI
Herrero, M. A.; Velázquez, J. J. L. Generic behaviour of one-dimensional blow up patterns. (English) Zbl 0798.35081 Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 19, No. 3, 381-450 (1992). Reviewer: L.Recke (Berlin) MSC: 35K60 35B40 35K15 × Cite Format Result Cite Review PDF Full Text: Numdam EuDML