Sixth-order Parabolic Equation Research Articles

Sixth-order parabolic equation on an interval: Eigenfunction expansion, Green’s function, and intermediate asymptotics for a finite thin film with elastic resistance

Sixth-order parabolic equation on an interval: Eigenfunction expansion, Green’s function, and intermediate asymptotics for a finite thin film with elastic resistance

Global dynamics of solutions for a sixth-order parabolic equation describing continuum evolution of film-free surface

This paper is concerned with a sixth-order diffusion equation, which describes continuum evolution of film-free surface. By using the regularity estimates for the semigroups, iteration technique and the classical existence theorem of global attractors we verified the existence of global attractor for this surface diffusion equation in the spaces H3(Ω) and fractional-order spaces Hk(Ω), where 0 ≤ k < ∞.

Blow-up and extinction for a sixth-order parabolic equation

In this paper, we consider an initial-boundary value problem for a sixth-order parabolic equation. We use the modified method of potential wells to study the relationship which the equation solutions existence, blow-up and the asymptotic behavior with initial conditions.

Asymptotic analysis of a thin fluid layer-elastic plate interaction problem

ABSTRACTWe study the nonstationary flow of an incompressible fluid in a thin rectangle with an elastic plate as the upper part of the boundary. The flow is governed by a time-dependent pressure drop and an external force and it is modeled by Stokes equations. The dynamic of this fluid–structure interaction problem is studied in the limit when the thickness of the fluid domain tends to zero. Using the asymptotic techniques, we obtain for the effective plate displacement a sixth-order parabolic equation with a non standard boundary conditions. Results on existence, uniqueness and regularity of the solution are proved. The approximation is justified through a weak convergence theorem.

Global weak solutions to a higher order nonlinear degenerate parabolic equation

Our aim in this paper is to investigate the existence for a sixth-order parabolic equation, which arises in oil-water-surfactant mixtures. More precisely, under suitable assumptions, first we study the existence and regularity of weak solutions to an initial–boundary problem for a non-degenerate sixth-order parabolic equation. Second considering the limits of the solutions obtained in the first step, we prove the existence of weak solutions.