Inéquations variationnelles d'évolution paraboliques du 2ème ordre
Inertial manifolds of damped semilinear wave equations
Infinite systems of strong parabolic differential-functional inequalities.
Influence of diffusion on interactions between malignant gliomas and immune system
We analyse the influence of diffusion and space distribution of cells in a simple model of interactions between an activated immune system and malignant gliomas, among which the most aggressive one is GBM Glioblastoma Multiforme. It turns out that diffusion cannot affect stability of spatially homogeneous steady states. This suggests that there are two possible outcomes-the solution is either attracted by the positive steady state or by the semitrivial one. The semitrivial steady state describes...
Influence of Vibrations on Convective Instability of Reaction Fronts in Liquids
Propagation of polymerization fronts with liquid monomer and liquid polymer is considered and the influence of vibrations on critical conditions of convective instability is studied. The model includes the heat equation, the equation for the concentration and the Navier-Stokes equations considered under the Boussinesq approximation. Linear stability analysis of the problem is fulfilled, and the convective instability boundary is found depending on...
Influence of Vibrations on Convective Instability of Reaction Fronts in Porous Media
The aim of this paper is to study the effect of vibrations on convective instability of reaction fronts in porous media. The model contains reaction-diffusion equations coupled with the Darcy equation. Linear stability analysis is carried out and the convective instability boundary is found. The results are compared with direct numerical simulations.
Information denoising and quantization by diffusion reaction model.
Inhomogeneous Fractional Diffusion Equations
2000 Mathematics Subject Classification: Primary 26A33; Secondary 35S10, 86A05Fractional diffusion equations are abstract partial differential equations that involve fractional derivatives in space and time. They are useful to model anomalous diffusion, where a plume of particles spreads in a different manner than the classical diffusion equation predicts. An initial value problem involving a space-fractional diffusion equation is an abstract Cauchy problem, whose analytic solution can be written...
Inhomogeneous parabolic Neumann problems
Second order parabolic equations on Lipschitz domains subject to inhomogeneous Neumann (or, more generally, Robin) boundary conditions are studied. Existence and uniqueness of weak solutions and their continuity up to the boundary of the parabolic cylinder are proved using methods from the theory of integrated semigroups, showing in particular the well-posedness of the abstract Cauchy problem in spaces of continuous functions. Under natural assumptions on the coefficients and the inhomogeneity the...
Initial limits of temperatures on arbitrary open sets.
Initial-boundary value problem for some coupled nonlinear parabolic system of partial differential equations appearing in thermodiffusion in solid body.
Initial-boundary value problems in a plane corner for the heat equation.
Instabilities in a reaction diffusion model: spatially homogeneous and distributed systems.
Instability of traveling waves for a generalized diffusion model in population problems.
Instability of Turing type for a reaction-diffusion system with unilateral obstacles modeled by variational inequalities
We consider a reaction-diffusion system of activator-inhibitor type which is subject to Turing's diffusion-driven instability. It is shown that unilateral obstacles of various type for the inhibitor, modeled by variational inequalities, lead to instability of the trivial solution in a parameter domain where it would be stable otherwise. The result is based on a previous joint work with I.-S. Kim, but a refinement of the underlying theoretical tool is developed. Moreover, a different regime of parameters...
Instantaneous shrinking of the support for solutions to certain parabolic equations and systems
The paper contains conditions ensuring instantaneous shrinking of the support for solutions to semilinear parabolic equations with compactly supported coefficients of nonlinear terms and reaction-diffusion systems.
Integral manifold of the parabolic differential equation with deviating argument
Intégrales premières analytiques des équations différentielles paraboliques non linéaires et du système des équations de Navier-Stokes. Applications à la théorie des solutions statistiques et à d'autres problèmes
Integration of evolution equations in a locally convex space
Interaction of Periodic and Stationary Bifurcation from Multiple Eigenvalues.