Convergent semidiscretization of a nonlinear fourth order parabolic system

Convergent Semidiscretization of a Nonlinear Fourth Order Parabolic System

Long-time Behavior for a Nonlinear Fourth-order Parabolic Equation

We study the asymptotic behavior of solutions of the initialboundary value problem, with periodic boundary conditions, for a fourth-order nonlinear degenerate diffusion equation with a logarithmic nonlinearity. For strictly positive and suitably small initial data we show that a positive solution exponentially approaches its mean as time tends to infinity. These results are derived by analyzing...

A Nonlinear Fourth-order Parabolic Equation with Nonhomogeneous Boundary Conditions

Abstract. A nonlinear fourth-order parabolic equation with nonhomogeneous Dirichlet–Neumann boundary conditions in one space dimension is analyzed. This equation appears, for instance, in quantum semiconductor modeling. The existence and uniqueness of strictly positive classical solutions to the stationary problem are shown. Furthermore, the existence of global nonnegative weak solutions to the...

A Positivity-Preserving Numerical Scheme for a Nonlinear Fourth Order Parabolic System

Semidiscretization for a nonlocal parabolic problem

where u represents the temperature generated by the electric current flowing through a conductor, φ the electric potential, σ(u) and k(u) are, respectively, the electric and thermal conductivities. For more description, we refer to [5, 6, 7, 8, 11] among others. We recall also that the Euler forward method was used by several authors to treat semidiscretization of nonlinear parabolic problems, ...