The Hierarchical Basis Multigrid Method.
The hierarchical basis multigrid method for convection-diffusion equations.
The Hirota method and soliton solutions to the multidimensional nonlinear Schrödinger equation.
The homogeneous balance of undetermined coefficients method and its application
The homogeneous balance of undetermined coefficients method is firstly proposed to solve such nonlinear partial differential equations (PDEs), the balance numbers of which are not positive integers. The proposed method can also be used to derive more general bilinear equation of nonlinear PDEs. The Eckhaus equation, the KdV equation and the generalized Boussinesq equation are chosen to illustrate the validity of our method. The proposed method is also a standard and computable method, which can...
The homogeneous Dirichlet problem for non-elliptic partial differential equations with strong nonlinearities
The Hopf bifurcation theorem for parabolic equations with infinite delay
The existence of the Hopf bifurcation for parabolic functional equations with delay of maximum order in spatial derivatives is proved. An application to an integrodifferential equation with a singular kernel is given.
The h-p Version of the Finite Element Method for Elliptic Equations of Order 2m.
The H-theorem for Boltzmann type equations.
The impact of unbounded swings of the forcing term on the asymptotic behavior of functional equations
Necessary and sufficient conditions have been found to force all solutions of the equation to behave in peculiar ways. These results are then extended to the elliptic equation where is the Laplace operator and is an integer.
The index of isolated critical points and solutions of elliptic equations in the plane
The Indicatrix Method in Free Boundary Problems.
The inhomogeneous dam problem with discontinuous permeability
The initial boundary value problem for the high order parabolic equation in unbounded domain.
The initial boundary value problem of a mixed-typed hemivariational inequality.
The initial value problem for parabolic equations with data in
The initial value problem for the equations of magnetohydrodynamic type in non-cylindrical domains.
By using the spectral Galerkin method, we prove the existence of weak solutions for a system of equations of magnetohydrodynamic type in non-cylindrical domains.
The initial value problem of the Poincaré gauge theory in vacuum. II. First order formalism
The initial value problem of the Poincaré gauge theory in vacuum. I. Second order formalism
The initial-boundary value problem for some pseudoparabolic system in unbounded domain.
The initial-boundary value problem for the non-barotropic compressible Euler equations : structural-stability and data dependence