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math.AP2022
Gradient profile for the reconnection of vortex lines with the boundary in type-II superconductors
Yi C. Huang, Hatem Zaag
In a recent work, Duong, Ghoul and Zaag determined the gradient profile for blowup solutions of standard semilinear heat equation with power nonlinearities in the (supposed to be)…
math.AP2022
Modulation theory for the flat blowup solutions of nonlinear heat equation
Giao Ky Duong, Nejla Nouaili, Hatem Zaag
In this paper, we revisit the proof of the existence of a solution to the semilinear heat equation in one space dimension with a at blowup profile, already proved by Bricmont and K…
math.AP2022
On degenerate blow-up profiles for the subcritical semilinear heat equation
Frank Merle, Hatem Zaag
We consider the semilinear heat equation with a superlinear power nonlinearity in the Sobolev subcritical range. We construct a solution which blows up in finite time only at the o…