A posteriori error estimates of the discontinuous Galerkin method for the heat conduction equation
A priori bounds for solutions of parabolic problems and applications
A remark on a parabolic problem in a sectorial domain.
A semidiscretization scheme for a phase-field type model for solidification.
A strong solution of an evolution problem with integral conditions.
A technique of upstream type applied to a linear nonconforming finite element approximation of convective diffusion equations
A temperature control problem.
A variational approach to the theory of temperature boundary layer.
A variational inequality for discontinuous solutions of degenerate parabolic equations.
The Beltrami framework for image processing and analysis introduces a non-linear parabolic problem, called in this context the Beltrami flow. We study in the framework for functions of bounded variation, the well-posedness of the Beltrami flow in the one-dimensional case. We prove existence and uniqueness of the weak solution using lower semi-continuity results for convex functions of measures. The solution is defined via a variational inequality, following Temam?s technique for the evolution problem...
A variational method for parameter identification
Absolute continuity for elliptic-caloric measures
A Carleson condition on the difference function for the coefficients of two elliptic-caloric operators is shown to give absolute continuity of one measure with respect to the other on the lateral boundary. The elliptic operators can have time dependent coefficients and only one of them is assumed to have a measure which is doubling. This theorem is an extension of a result of B. Dahlberg [4] on absolute continuity for elliptic measures to the case of the heat equation. The method of proof is an...
Alternating direction Galerkin method with capacitance matrix for the parabolic problem with natural boundary condition
An elementary approach to nonexistence of solutions of linear parabolic equations
This note presents an elementary approach to the nonexistence of solutions of linear parabolic initial-boundary value problems considered in the Feller test.
An enclosure generating modification of the method of discretization in time
An endpoint Littlewood-Paley inequality for BVP associated with the Laplacian on Lipschitz domains.
We prove a commutator inequality of Littlewood-Paley type between partial derivatives and functions of the Laplacian on a Lipschitz domain which gives interior energy estimates for some BVP. It can be seen as an endpoint inequality for a family of energy estimates.
An extension of Rothe's method to non-cylindrical domains
In this paper Rothe’s classical method is extended so that it can be used to solve some linear parabolic boundary value problems in non-cylindrical domains. The corresponding existence and uniqueness theorems are proved and some further results and generalizations are discussed and applied.
An Isoperimetric Inequality for the Principal Eigenvalue of a Periodic-Parabolic Problem.
An -approach for the study of degenerate parabolic equations.
An observability estimate for parabolic equations from a measurable set in time and its applications
This paper presents a new observability estimate for parabolic equations in , where is a convex domain. The observation region is restricted over a product set of an open nonempty subset of and a subset of positive measure in . This estimate is derived with the aid of a quantitative unique continuation at one point in time. Applications to the bang-bang property for norm and time optimal control problems are provided.
An operator-splitting Galerkin/SUPG finite element method for population balance equations : stability and convergence
We present a heterogeneous finite element method for the solution of a high-dimensional population balance equation, which depends both the physical and the internal property coordinates. The proposed scheme tackles the two main difficulties in the finite element solution of population balance equation: (i) spatial discretization with the standard finite elements, when the dimension of the equation is more than three, (ii) spurious oscillations in the solution induced by standard Galerkin approximation...