Schéma des différences finies pour un système d'équations paraboliques non linéaires avec dérivées mixtes
Segmentation of MRI data by means of nonlinear diffusion
The article focuses on the application of the segmentation algorithm based on the numerical solution of the Allen-Cahn non-linear diffusion partial differential equation. This equation is related to the motion of curves by mean curvature. It exhibits several suitable mathematical properties including stable solution profile. This allows the user to follow accurately the position of the segmentation curve by bringing it quickly to the vicinity of the segmented object and by approaching the details...
Semidiscretization for a nonlocal parabolic problem.
Short-time heat flow and functions of bounded variation in
We prove a characterisation of sets with finite perimeter and functions in terms of the short time behaviour of the heat semigroup in . For sets with smooth boundary a more precise result is shown.
Simultaneous versus nonsimultaneous blowup for a system of heat equations coupled boundary flux.
Skipping transition conditions in a posteriori error estimates for finite element discretizations of parabolic equations
In this paper we derive a posteriori error estimates for the heat equation. The time discretization strategy is based on a θ-method and the mesh used for each time-slab is independent of the mesh used for the previous time-slab. The novelty of this paper is an upper bound for the error caused by the coarsening of the mesh used for computing the solution in the previous time-slab. The technique applied for deriving this upper bound is independent of the problem and can be generalized to other time...
Solution of some parabolic integro-differential equations by means of the algebraic operational calculus of distributions.
Solution to a parabolic equation with integral type boundary condition.
Solutions Of Some Parabolic Integro-Differential Equations By Means Of The Algebraic Operational Calculus Of Distributions
Solvability in Sobolev spaces of a problem for a second order parabolic equation with time derivative in the boundary condition.
Solvability of a coupled system of parabolic and ordinary differential equations
A model of coupled parabolic and ordinary differential equations for a heterogeneous catalytic reaction is considered and the existence and uniqueness theorem of the classic solution is proved.
Solvability of a mathematical model of dissociative adsorption and associative desorption type
A mathematical model of dissociative adsorption and associative desorption for diatomic molecules is generalized. The model is described by a coupled system of parabolic and ordinary differential equations. The existence and uniqueness theorem of the classical solution is proved.
Solvability of degenerated parabolic equations without sign condition and three unbounded nonlinearities.
Solvability of the heat equation in weighted Sobolev spaces
The existence of solutions to an initial-boundary value problem to the heat equation in a bounded domain in ℝ³ is proved. The domain contains an axis and the existence is proved in weighted anisotropic Sobolev spaces with weight equal to a negative power of the distance to the axis. Therefore we prove the existence of solutions which vanish sufficiently fast when approaching the axis. We restrict our considerations to the Dirichlet problem, but the Neumann and the third boundary value problems can...
Solvability of the inverse problem of finding thermal conductivity.
Some classes of inverse evolution problems for parabolic equations.
Some Fractional Extensions of the Temperature Field Problem in Oil Strata
This survey is devoted to some fractional extensions of the incomplete lumped formulation, the lumped formulation and the formulation of Lauwerier of the temperature field problem in oil strata. The method of integral transforms is used to solve the corresponding boundary value problems for the fractional heat equation. By using Caputo’s differintegration operator and the Laplace transform, new integral forms of the solutions are obtained. In each of the different cases the integrands are expressed...
Some properties of solutions for a class of metaparabolic equations.
Some properties of weighted Sobolev spaces in
Source localization and sensor placement in environmental monitoring
In this paper we discuss two closely related problems arising in environmental monitoring. The first is the source localization problem linked to the question How can one find an unknown "contamination source"? The second is an associated sensor placement problem: Where should we place sensors that are capable of providing the necessary "adequate data" for that? Our approach is based on some concepts and ideas developed in mathematical control theory of partial differential equations.