A 2D climate energy balance model coupled with a 3D deep ocean model.
A blow up condition for a nonautonomous semilinear system.
A boundary control problem with a nonlinear reaction term.
A Cauchy problem for . Asymptotic behaviour of solutions
A cell complex structure for the space of heteroclines for a semilinear parabolic equation.
A class of time discrete schemes for a phase-field system of Penrose-Fife type
A class of time discrete schemes for a phase–field system of Penrose–Fife type
In this paper, a phase field system of Penrose–Fife type with non–conserved order parameter is considered. A class of time–discrete schemes for an initial–boundary value problem for this phase–field system is presented. In three space dimensions, convergence is proved and an error estimate linear with respect to the time–step size is derived.
A combustion model with unbounded thermal conductivity and reactant diffusivity in non-smooth domains.
A comment on the Jäger-Kačur's linearization scheme for strongly nonlinear parabolic equations
The aim of this paper is to demonstrate how the variational equations from can be formulated and solved in some abstract Banach spaces without any a priori construction of special linearization schemes. This should be useful e.g. in the analysis of heat conduction problems and modelling of flow in porous media.
A comparison principle for a class of subparabolic equations in Grushin-type spaces.
A computational approach to fractures in crystal growth
In the present paper, we motivate and describe a numerical approach in order to detect the creation of fractures in a facet of a crystal evolving by anisotropic mean curvature. The result appears to be in accordance with the known examples of facet-breaking. Graphical simulations are included.
A Construction of Stable Subharmonic Orbits in Monotone Time-periodic Dynamical Systems.
A coupled Cahn-Hilliard particle system.
A degenerate parabolic system for three-phase flows in porous media
A classical model for three-phase capillary immiscible flows in a porous medium is considered. Capillarity pressure functions are found, with a corresponding diffusion-capillarity tensor being triangular. The model is reduced to a degenerate quasilinear parabolic system. A global existence theorem is proved under some hypotheses on the model data.
A description of blow-up for the solid fuel ignition model
A description of self-similar blow-up for dimensions
A dual mesh method for a nonlocal thermistor problem.
A finite difference method for quasi-linear and nonlinear differential functional parabolic equations with Dirichlet's condition
We deal with a finite difference method for a wide class of nonlinear, in particular strongly nonlinear or quasi-linear, second-order partial differential functional equations of parabolic type with Dirichlet's condition. The functional dependence is of the Volterra type and the right-hand sides of the equations satisfy nonlinear estimates of the generalized Perron type with respect to the functional variable. Under the assumptions adopted, quasi-linear equations are a special case of nonlinear...
A finite element scheme for the evolution of orientational order in fluid membranes
We investigate the evolution of an almost flat membrane driven by competition of the homogeneous, Frank, and bending energies as well as the coupling of the local order of the constituent molecules of the membrane to its curvature. We propose an alternative to the model in [J.B. Fournier and P. Galatoa, J. Phys. II7 (1997) 1509–1520; N. Uchida, Phys. Rev. E66 (2002) 040902] which replaces a Ginzburg-Landau penalization for the length of the order parameter by a rigid constraint. We introduce...
A finite element solution of the monlinear heat equation