Modulation theory for the flat blow-up solutions of nonlinear heat equation

Refined asymptotics for the blow-up solution of the complex Ginzburg–Landau equation in the subcritical case

“…To end the proof we estimate ş |y|ą1 H n N ρ s dy. By Lemma 5.5, the definition of V A,γ,b 0 ,θ 0 psq and using Lemma A.2 from[9], we get ˇˇˇˇż…”

“…The study of such linearisation will simplify the computations as you will see in section 5. ‚ Our construction in this work is inspired by the work of Bricmont and Kupiainen in [3] and our recent result [9]. But this is far from being a simple adaptation of the construction made in the case of the nonlinear heat equation because of the complex structure of the CGL equation 2.1.…”