Convergence to the Poisson kernel for the Laplace equation with a nonlinear dynamical boundary condition

Asymptotic analysis for the eikonal equation with the dynamical boundary conditions

“…We are also motivated by the recent studies on the Laplace equation with the nonlinear dynamical boundary condition of the type due to Amann‐Fila , Fila‐Ishige‐Kawakami and others, where the blow‐up phenomena and large time behavior of solutions are investigated. The Laplace equation above is, of course, the limit equation of the heat equations in as .…”

Asymptotics for a nonlinear integral equation with a generalized heat kernel

“…• (Fractional semilinear parabolic equation) 4) where N ≥ 1, 0 < θ < 2 and p > 1 + θ/N (see e.g. [1], [13], [14], [19] and [32]);…”

Asymptotic behavior and decay estimates of the solutions for a nonlinear parabolic equation with exponential nonlinearity

“…for all t ≥ T 1 . Therefore, applying an argument similar to the proof of Theorem 1.1 in [5] with (2.9) and (2.10), we have (2.11), and the proof of Theorem 2.4 is complete. ✷…”