Long-time behavior for a nonlinear fourth-order parabolic equation

50 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Exponential decay toward equilibrium via entropy methods for reaction–diffusion equations (2006, methodology): “The entropy method has lately been used in many situations: nonlinear diffusion equations (such as fast diffusions [9,10], equations of fourth order [5], Landau equation [13], etc.”
Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds (2008, methodology): “Next, for any s ∈ [2, 3), ‖a1a3 − a2a4‖L s 2 ([0,T ]×[0,1]) ≤ C15 (1 + T 2 s ) .”
The Wasserstein Gradient Flow of the Fisher Information and the Quantum Drift-diffusion Equation (2009, background): “Besides the possibility to get crucial a priori estimates, these functionals have also been extremely useful to study asymptotic behavior of the solutions (as in [ 15 ,24]), since convergence to the constant steady state can be derived by studying the precise rate of decay of Lyapunov functionals.”