A remark on a parabolic problem in a sectorial domain.
A remark on approximate solving of a class of initial-boundary value problems
A remark on parabolic equations.
A remark on the large time behavior of solutions of viscous Hamilton-Jacobi equations
A remark on the note : “Partial Hölder continuity of the spatial derivatives of the solutions to nonlinear parabolic systems with quadratic growth”
A remark on the stability of stationary solutions of parabolic variational inequalities
A remark on the uniqueness of fundamental solutions to the -Laplacian equation, .
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.
A result of existence for an original convection-diffusion equation.
En este artículo se estudia el análisis matemático de una ley de conservación que no es clásica. El modelo describe procesos estatigráficos en Geología y tiene en cuenta una condición de tasa de erosión limitada. En primer lugar se presentan el modelo físico y la formulación matemática (posiblemente nueva). Tras enunciar la definición solución se presentan las herramientas que permiten probar la existencia de soluciones.
A Riccati equation arising in a boundary control problem for distributed parameters
Si prova resistenza locale della soluzione di una equazione di Riccati che si incontra in un problema di controllo ottimale. In ipotesi di regolarità per il costo si prova resistenza globale. Il problema astratto considerato è il modello di alcuni problemi di controllo ottimale governati da equazioni paraboliche con controllo sulla frontiera.
A Schwarz auditive method with high order interface conditions and nonoverlapping subdomains
A semidiscretization scheme for a phase-field type model for solidification.
A semilinear parabolic boundary-value problem in bioreactors theory.
A simple bioclogging model that accounts for spatial spreading of bacteria.
A simple regularization method for the ill-posed evolution equation
The nonhomogeneous backward Cauchy problem , where is a positive self-adjoint unbounded operator which has continuous spectrum and is a given function being given is regularized by the well-posed problem. New error estimates of the regularized solution are obtained. This work extends earlier results by N. Boussetila and by M. Denche and S. Djezzar.
A simple-minded computation of heat kernels on Heisenberg groups
We compute the heat kernel on the classical and nonisotropic Heisenberg groups, and on the free step two nilpotent groups , by an elementary method, in particular without using Laguerre calculus.
A singular radially symmetric problem in electrolytes theory
Existence of radially symmetric solutions (both stationary and time dependent) for a parabolic-elliptic system describing the evolution of the spatial density of ions in an electrolyte is studied.
A solution of nonlinear diffusion problems by semilinear reaction-diffusion systems
This paper deals with nonlinear diffusion problems involving degenerate parabolic problems, such as the Stefan problem and the porous medium equation, and cross-diffusion systems in population ecology. The degeneracy of the diffusion and the effect of cross-diffusion, that is, nonlinearities of the diffusion, complicate its analysis. In order to avoid the nonlinearities, we propose a reaction-diffusion system with solutions that approximate those of the nonlinear diffusion problems. The reaction-diffusion...
A solution of the boundary value problem in heat conduction
A Spatial Model of Tumor Growth with Cell Age, Cell Size, and Mutation of Cell Phenotypes
A model of tumor growth in a spatial environment is analyzed. The model includes proliferating and quiescent compartments of tumor cells indexed by successively mutated cell phenotypes of increasingly proliferative aggressiveness. The model incorporates spatial dependence due to both random motility and directed movement haptotaxis. The model structures tumor cells by both cell age and cell size. The model consists of a system of nonlinear partial differential equations for the compartments of...