A partial solution for Feynman's problem – a new derivation of the Weyl equation.
A Partial Solution of the Pompeiu Problem.
A partially ordered space connected with the de la Vallée Poussin problem
A Particle Method for First-order Symmetric Systems.
A Particle Method to Solve the Navier-Stokes System.
A pathwise solution for nonlinear parabolic equations with stochastic perturbations
We analyse here a semilinear stochastic partial differential equation of parabolic type where the diffusion vector fields are depending on both the unknown function and its gradient ∂ xu with respect to the state variable, ∈ ℝn. A local solution is constructed by reducing the original equation to a nonlinear parabolic one without stochastic perturbations and it is based on a finite dimensional Lie algebra generated by the given diffusion vector fields.
A pattern formation problem on the sphere.
A PDE approach to certain large deviation problems for systems of parabolic equations
A penalty method for approximations of the stationary power-law Stokes problem.
A Penalty Method for the Approximate Solution of Stationary Maxwell Equations.
A penalty method for the time-dependent Stokes problem with the slip boundary condition and its finite element approximation
We consider the finite element method for the time-dependent Stokes problem with the slip boundary condition in a smooth domain. To avoid a variational crime of numerical computation, a penalty method is introduced, which also facilitates the numerical implementation. For the continuous problem, the convergence of the penalty method is investigated. Then we study the fully discretized finite element approximations for the penalty method with the P1/P1-stabilization or P1b/P1 element. For the discretization...
A penalty method for topology optimization subject to a pointwise state constraint
This paper deals with topology optimization of domains subject to a pointwise constraint on the gradient of the state. To realize this constraint, a class of penalty functionals is introduced and the expression of the corresponding topological derivative is obtained for the Laplace equation in two space dimensions. An algorithm based on these concepts is proposed. It is illustrated by some numerical applications.
A perspective on the contributions of Alan C. Lazer to critical point theory.
A perturbation problem with two small parameters in the framework of the heat conduction of a fiber reinforced body
A Petrov-Galerkin approximation of convection-diffusion and reaction-diffusion problems
A general construction of test functions in the Petrov-Galerkin method is described. Using this construction; algorithms for an approximate solution of the Dirichlet problem for the differential equation are presented and analyzed theoretically. The positive number is supposed to be much less than the discretization step and the values of . An algorithm for the corresponding two-dimensional problem is also suggested and results of numerical tests are introduced.
A phase-field model of grain boundary motion
We consider a phase-field model of grain structure evolution, which appears in materials sciences. In this paper we study the grain boundary motion model of Kobayashi-Warren-Carter type, which contains a singular diffusivity. The main objective of this paper is to show the existence of solutions in a generalized sense. Moreover, we show the uniqueness of solutions for the model in one-dimensional space.
A Phragmén - Lindelöf Principle for Subsolutions of Quasi - Linear Equations.
A Picard-Maclaurin theorem for initial value PDEs.
A piecewise P2-nonconforming quadrilateral finite element
We introduce a piecewise P2-nonconforming quadrilateral finite element. First, we decompose a convex quadrilateral into the union of four triangles divided by its diagonals. Then the finite element space is defined by the set of all piecewise P2-polynomials that are quadratic in each triangle and continuously differentiable on the quadrilateral. The degrees of freedom (DOFs) are defined by the eight values at the two Gauss points on each of the four edges plus the value at the intersection of the...
A polyharmonic analogue of a Lelong theorem and polyhedric harmonicity cells.