PML technique and non-local boundary conditions for the parabolic equation;

High order parabolic equation algorithm and its application to non-local boundary condition;

Considering a reaction-diffusion equation with non-local boundary conditions in bounded regions, we have found under some conditions the solutions of the equation blow up or exist globally.

For solving more complicated heat conduction problems with time-dependent boundary conditions,it can be beneficial and essential to transformation of heat conduction differential equation to integral one.

Existence of global attractor for reaction-diffusion equations under nonlinear boundary conditions;

By employing Galerkin approach,the authors have proved the existence and uniqueness of the global solutions to the equation hereinabove under nonlinear boundary condition,and proved the continuous dependence of the soluti.

In this paper, we use the theory of differential inequalities to study the sigular perturbation for a class of higher order nonlinear equations with nonlinear boundary conditions.

Existence and uniqueness of nonnegative classical solution for a parabolic system with nonlinear boundary conditions;

Global existence and blow-up problem for nonlinear parabolic equations with nonlinear boundary conditions;

The existence of the global solution for the system under some certain initial and nonlinear boundary conditions is proved use Faedo-Galerkin method.

We study the existence of a class of nonlinear elliptic equations with non-homogeneous boundary conditions by using variational methods for the various cases that λ,μ∈R and 1<p,q<2N/(N-2).

By using the upper and lower solutions method,the existence of solutions was studied for a type of second-order two-points boundary value problems with p-Laplacian operator under non-homogeneous boundary conditions.