Solutions to time-fractional diffusion-wave equation in cylindrical coordinates.
Solutions which are flat or Singular on Totally Characteristic Manifolds of first order Partial Differential Equations
Solvability for a class of non-homogeneous differential operators on two-step nilpotent groups.
Solvability of invariant sublaplacians on spheres and group contractions
In the first part of this paper we study the local and global solvability and the hypoellipticity of a family of left-invariant sublaplacians on the spheres . In the second part, we introduce a larger family of left-invariant sublaplacians on and study the corresponding properties by means of a Lie group contraction to the Heisenberg group.
Solving heat and wave-like equations using He's polynomials.
Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method
The Cahn-Hilliard variational inequality is a non-standard parabolic variational inequality of fourth order for which straightforward numerical approaches cannot be applied. We propose a primal-dual active set method which can be interpreted as a semi-smooth Newton method as solution technique for the discretized Cahn-Hilliard variational inequality. A (semi-)implicit Euler discretization is used in time and a piecewise linear finite element discretization of splitting type is used in space leading...
Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method
The Cahn-Hilliard variational inequality is a non-standard parabolic variational inequality of fourth order for which straightforward numerical approaches cannot be applied. We propose a primal-dual active set method which can be interpreted as a semi-smooth Newton method as solution technique for the discretized Cahn-Hilliard variational inequality. A (semi-)implicit Euler discretization is used in time and a piecewise linear finite element discretization of splitting type is used in space...
Some aspects of holomorphic approximations from the point of view of PDEs
Some asymptotic error estimates for finite element approximation of minimal surfaces
Some critical point theorems and applications to semilinear elliptic partial differential equations
Some decay properties for the damped wave equation on the torus
This article is a proceedings version of the ongoing work [1], and has been the object of a talk of the second author during the Journées “Équations aux Dérivées Partielles” (Biarritz, 2012).We address the decay rates of the energy of the damped wave equation when the damping coefficient does not satisfy the Geometric Control Condition (GCC). First, we give a link with the controllability of the associated Schrödinger equation. We prove that the observability of the Schrödinger group implies that...
Some estimates of Schrödinger-type operators with certain nonnegative potentials.
Some estimates of solutions to Monge-Ampère type equations in dimension two
Some exact estimates of weak solutions to a mixed boundary value problem for nonlinear equations in domains with nonsmooth boundary.
Some exact Solutions of the Korteweg-de Vries Equation with Variable Coefficients
Some geometric aspects of the calculus of variations in several independent variables
This paper describes some recent research on parametric problems in the calculus of variations. It explains the relationship between these problems and the type of problem more usual in physics, where there is a given space of independent variables, and it gives an interpretation of the first variation formula in this context in terms of cohomology.
Some Linear Elliptic Selfsimilar Equations with Whirl-Like Solutions.
Some notes to certain modification of the Oseen problem
Some notes to the transport equation and to the Green formula
Some properties of stationary parabolic mixed problems in an infinite cylinder