A new look at boundary perturbations of generators.
A new version of the fast Gauss transform.
A nonhomogeneous backward heat problem: regularization and error estimates.
A note of uniqueness on the Cauchy problem for Schrödinger or heat equations with degenerate elliptic principal parts
We study the local uniqueness in the Cauchy problem for Schrödinger or heat equations whose principal parts are nonnegative. We show the compact uniqueness under a weak form of pseudo convexity. This makes up for the known results under the conormal pseudo convexity given by Tataru, Hörmander, Robbiano- Zuily and L. T'Joen. Our method is based on a kind of integral transform and a weak form of Carleman estimate for degenerate elliptic operators.
A note on a heat potential and the parabolic variation
A note on asymptotic expansion for a periodic boundary condition
The aim of this contribution is to present a new result concerning asymptotic expansion of solutions of the heat equation with periodic Dirichlet–Neuman boundary conditions with the period going to zero in D.
A note on the approximation of free boundaries by finite element methods
A note on the convexity theorem for mean values of subtemperatures.
A note on the parabolic variation
A condition for solvability of an integral equation which is connected with the first boundary value problem for the heat equation is investigated. It is shown that if this condition is fulfilled then the boundary considered is -Holder. Further, some simple concrete examples are examined.
A note to the theory of periodic solutions of a parabolic equation
A numerical scheme for the two phase Mullins-Sekerka problem.
A posteriori error estimates for a nonconforming finite element discretization of the heat equation
The paper presents an a posteriori error estimator for a (piecewise linear) nonconforming finite element approximation of the heat equation in , or 3, using backward Euler’s scheme. For this discretization, we derive a residual indicator, which use a spatial residual indicator based on the jumps of normal and tangential derivatives of the nonconforming approximation and a time residual indicator based on the jump of broken gradients at each time step. Lower and upper bounds form the main results...
A posteriori error estimates for a nonconforming finite element discretization of the heat equation
The paper presents an a posteriori error estimator for a (piecewise linear) nonconforming finite element approximation of the heat equation in , d=2 or 3, using backward Euler's scheme. For this discretization, we derive a residual indicator, which use a spatial residual indicator based on the jumps of normal and tangential derivatives of the nonconforming approximation and a time residual indicator based on the jump of broken gradients at each time step. Lower and upper bounds form the main...
A posteriori error estimates of the discontinuous Galerkin method for the heat conduction equation
A posteriori upper and lower error bound of the high-order discontinuous Galerkin method for the heat conduction equation
We deal with the numerical solution of the nonstationary heat conduction equation with mixed Dirichlet/Neumann boundary conditions. The backward Euler method is employed for the time discretization and the interior penalty discontinuous Galerkin method for the space discretization. Assuming shape regularity, local quasi-uniformity, and transition conditions, we derive both a posteriori upper and lower error bounds. The analysis is based on the Helmholtz decomposition, the averaging interpolation...
A priori estimates in weighted spaces for solutions of the Poisson and heat equations
We prove a priori estimates for solutions of the Poisson and heat equations in weighted spaces of Kondrat'ev type. The weight is a power of the distance from a distinguished axis.
A problem of thermal shock with thermal relaxation.
A remark on a Harnack inequality for degenerate parabolic equations
A remark on a parabolic problem in a sectorial domain.
A remarkably interesting, simple P.D.E.
In this note, I will summarize and make a couple of small additions to some results which I obtained earlier with David Williams in [1]. Williams and I hope to expand and refine these additions in a future paper based on work that is still in process.