In this paper, we consider numerical approximations for the viscous Cahn–Hilliard equation
with hyperbolic relaxation. This type of equations processes energy-dissipative structure …

In this article, we derive error estimates for two second-order numerical schemes for solving
the viscous Cahn-Hilliard equation with hyperbolic relaxation, one based on the second …

Solvability of Cauchy's problem in R 2 for subcritical quasi-geostrophic equation is
discussed here in two phase spaces; L p (R 2) with p> 2 2 α− 1 and H s (R 2) with s> 1. A …

Abstract We consider the Navier–Stokes equation (NS) in dimensions two and three as limits
of the fractional approximations. In 2-D the NS problem is critical with respect to the standard …

Solvability of Cauchyʼs problem in RN for an extended viscous Cahn–Hilliard equation is
studied. The problem is considered first in a standard Sobolev space H1 (RN), next a notion …

In this paper, we construct new first-order and second-order time stepping schemes, which
are based on the newly developed the scalar auxiliary variable (SAV) approach, for solving …

In this paper we exhibit the dissipative mechanism of the Cahn–Hilliard equation in H1 (RN).
We show a weak form of dissipativity by showing that each individual solution is attracted, in …

This paper is concerned with the initial-boundary value problem for the hyperbolic relaxation
of the Cahn-Hilliard/Allen-Cahn equation with a proliferation term, in an arbitrary two …

This self-contained book covers the theory of semilinear equations with sectorial operator
going back to the studies of Yosida, Henry, and Pazy, which are deeply extended nowadays …

We study the well-posedness and asymptotic behavior of solutions to the Cauchy problem of
a three-dimensional sixth-order Cahn–Hilliard equation arising in oil-water-surfactant …