A minmax problem for parabolic systems with competitive interactions.
A mixed-culture model of a probiotic biofilm control system.
A model of evolution of temperature and density of ions in an electrolyte
We study existence and nonexistence of solutions (both stationary and evolution) for a parabolic-elliptic system describing the electrodiffusion of ions. In this model the evolution of temperature is also taken into account. For stationary states the existence of an external potential is also assumed.
A model of frontal polymerization including the gel effect.
A model of frontal polymerization using complex initiation.
A new approach to initial traces in nonlinear filtration
A new Monte Carlo method for solving a stationary diffusion equation.
A nonlocal coagulation-fragmentation model
A new nonlocal discrete model of cluster coagulation and fragmentation is proposed. In the model the spatial structure of the processes is taken into account: the clusters may coalesce at a distance between their centers and may diffuse in the physical space Ω. The model is expressed in terms of an infinite system of integro-differential bilinear equations. We prove that some results known in the spatially homogeneous case can be extended to the nonlocal model. In contrast to the corresponding local...
A note on Chebyshev series solution of the Crank-Gupta equation.
A note on the paper of Y. Naito
This note contains some remarks on the paper of Y. Naito concerning the parabolic system of chemotaxis and published in this volume.
A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations
This paper is devoted to the study of a posteriori error estimates for the scalar nonlinear convection-diffusion-reaction equation . The estimates for the error between the exact solution and an upwind finite volume approximation to the solution are derived in the -norm, independent of the diffusion parameter . The resulting a posteriori error estimate is used to define an grid adaptive solution algorithm for the finite volume scheme. Finally numerical experiments underline the applicability...
A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations
This paper is devoted to the study of a posteriori error estimates for the scalar nonlinear convection-diffusion-reaction equation . The estimates for the error between the exact solution and an upwind finite volume approximation to the solution are derived in the L1-norm, independent of the diffusion parameter D. The resulting a posteriori error estimate is used to define an grid adaptive solution algorithm for the finite volume scheme. Finally numerical experiments underline the applicability...
A priori bounds and global existence for a strongly coupled quasilinear parabolic system modeling chemotaxis.
A problem of thermal shock with thermal relaxation.
A reaction-diffusion equation on a net-shaped thin domain
A Reduced Model for Flame-Flow Interaction
The paper is concerned with an extension of the classical relation between the flame speed and the curvature-flow stretch, valid only for high Lewis numbers (diffusively stable flames). At low Lewis numbers the corresponding flame-flow system suffers short-wavelength instability, making the associated initial value problem ill-posed. In this study the difficulty is resolved by incorporation of higher-order effects. As a result one ends up with a reduced model based on a coupled system of second-order...
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 spatially inhomogeneous diffusion problem with strong absorption
We study the asymptotic behaviour () of the solutions of a nonlinear diffusion problem with strong absorption. We prove convergence to the stationary solution in the by means of an appropriate family of sub and supersolutions. In appendix we prove the well posedness of the problem.
A transient density-dependent diffusion-reaction model for the limitation of antibiotic penetration in biofilms.
A variational approach to bifurcation in reaction-diffusion systems with Signorini type boundary conditions
We consider a simple reaction-diffusion system exhibiting Turing's diffusion driven instability if supplemented with classical homogeneous mixed boundary conditions. We consider the case when the Neumann boundary condition is replaced by a unilateral condition of Signorini type on a part of the boundary and show the existence and location of bifurcation of stationary spatially non-homogeneous solutions. The nonsymmetric problem is reformulated as a single variational inequality with a potential...