Research interest:
The formation of singularities in finite time play an important role in problems arising from Physics and Biology.
My research focuses on understanding the behaviour of solutions near singularity to certain parabolic equations, wave equations, Complex Ginzburg Landau and Keller-Segel equations.
My research focuses on understanding the behaviour of solutions near singularity to certain parabolic equations, wave equations, Complex Ginzburg Landau and Keller-Segel equations.
Preprints and publications:
. Construction of type-I-Log Blowup for the Keller-Segel system in dimensions 3 and 4,
with Van Tien Nguyen and Hatem Zaag, submitted, (2023).arxiv.org/abs/2309.13932
. Flat blow-up solutions for the complex Ginzburg Landau equation,
with Giao Ky Doung and Hatem Zaag, submitted, (2023), arxiv.org/abs/2308.02297 .
. Modulation theory for the flat blow-up solutions of nonlinear heat equation,
with Giao Ky Doung and Hatem Zaag, Commun.Pure.Appl.Anal, (2023), to appear, arxiv.org/abs/2206.04378.
. Refined asymptotic for the blow-up solution of the Complex Ginzburg Landau equation in a the subcritial case.
with Giao Ky Doung and Hatem Zaag, Ann.I.H.Poincaré-AN, no. 39, (2022) 41-85.
. Construction of a blow-up solution for the Complex Ginzburg Landau equation in a critical case $\beta\not =0$.
with Giao Ky Doung and Hatem Zaag, Mem.Amer.Math.Soc,285 285 (2023), no.1411, arxiv.org/abs/1912.05922.
. Construction of a blow-up solution for the Complex Ginzburg Landau equation in some critical case.
with Hatem Zaag . Arch. Rat. Mech. Anal. (2018),no. 3, 995-1058, on arxiv.org.
. Construction of a stable periodic solution to a semilinear heat equation with a prescribed profile, with Fethi Mahmoudi and Hatem Zaag . Nonlinear Anal. 131 (2016), 300-324. on arxiv.org.
. Profile for a simultaneously blowing up solution for a complex valued semilinear heat equation, with Hatem Zaag. Comm. Partial Differential Equations 40 (2015), 1197-1217. on arxiv.org.
. A Liouville theorem for a heat equation and applications for quenching. Nonlinearity 24(2011), no. 3, 797–832.
. A simplified proof of a Liouville theorem for nonnegative solution of a subcritical semilinear heat equations, Journal of dynamics and differential equations 21 (2009) no.1, 127--132. Erratum to ``A simplified proof of a Liouville theorem for nonnegative solution of a subcritical semilinear heat equation``(pdf).
. A Liouville theorem for vector valued semilinear heat equations with no gradient structure and applications to blow-up, with Hatem Zaag. Transactions of the AMS (2008).(PDF)
. C{1,a} regularity of the blow-up curve at non characteristic points for the one dimensional semilinear wave equation, Communications in partial differential equations 33 (2008), no.7-9, 1540--1548.
with Hatem Zaag . Arch. Rat. Mech. Anal. (2018),no. 3, 995-1058, on arxiv.org.
. Construction of a stable periodic solution to a semilinear heat equation with a prescribed profile, with Fethi Mahmoudi and Hatem Zaag . Nonlinear Anal. 131 (2016), 300-324. on arxiv.org.
. Profile for a simultaneously blowing up solution for a complex valued semilinear heat equation, with Hatem Zaag. Comm. Partial Differential Equations 40 (2015), 1197-1217. on arxiv.org.
. A Liouville theorem for a heat equation and applications for quenching. Nonlinearity 24(2011), no. 3, 797–832.
. A simplified proof of a Liouville theorem for nonnegative solution of a subcritical semilinear heat equations, Journal of dynamics and differential equations 21 (2009) no.1, 127--132. Erratum to ``A simplified proof of a Liouville theorem for nonnegative solution of a subcritical semilinear heat equation``(pdf).
. A Liouville theorem for vector valued semilinear heat equations with no gradient structure and applications to blow-up, with Hatem Zaag. Transactions of the AMS (2008).(PDF)
. C{1,a} regularity of the blow-up curve at non characteristic points for the one dimensional semilinear wave equation, Communications in partial differential equations 33 (2008), no.7-9, 1540--1548.