On a two-phase free boundary problem

The Dirichlet-to-Neumann map for the heat equation on a moving boundary

“…Indeed the curve + 12 (t) defined in (2.6) subdivides the domain 3 (t) into the two subdomains (1) 3 (t) and (2) 3 (t), see figure 4. The integral over the domain (2) 3 (t) equals f 4 .…”

“…Indeed the curve + 12 (t) defined in (2.6) subdivides the domain 3 (t) into the two subdomains (1) 3 (t) and (2) 3 (t), see figure 4. The integral over the domain (2) 3 (t) equals f 4 . Indeed, using the identity 2i dk R dk I = d k ∧ dk, as well as the complex form of Green's theorem in the domain (2) 3 (t) we find 2i…”

“…The integral over the domain (2) 3 (t) equals f 4 . Indeed, using the identity 2i dk R dk I = d k ∧ dk, as well as the complex form of Green's theorem in the domain (2) 3 (t) we find 2i…”

“…We consider the construction of the Dirichlet-to-Neumann map for the heat equation as a fundamental step toward the solution of inverse moving boundary problems for nonlinear diffusive equations. This applies in particular to the Burgers equation and to the nonlinear diffusion-convection equation [2,3].…”

Rogue wave triggered at a critical frequency of a nonlinear resonant medium

“…The integrability of the MB equations is given by ref. [36]. In our recent work, we have considered higher order dispersion and nonliner effects in the form of Maxwell-Bloch and Hirota equation and obtained the breathers, bright and dark rogue wave solutions [15].…”