Infinity Laplace equation with non-trivial right-hand side.
Influence of a boundary perforation on the Dirichlet energy
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.
Inhomogeneous boundary value problems for the von Kármán equations. II
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 boundary value problem for a system in elastodynamics with viscosity.
Initial boundary value problem for generalized Zakharov equations
This paper considers the existence and uniqueness of the solution to the initial boundary value problem for a class of generalized Zakharov equations in dimensions, and proves the global existence of the solution to the problem by a priori integral estimates and the Galerkin method.
Initial limits of temperatures on arbitrary open sets.
Initial traces of solutions to a one-phase Stefan problem in an infinite strip.
The main result of this paper is an integral estimate valid for non-negative solutions (with no reference to initial data) u ∈ L1loc (Rn x (0,T)) to(0.1) ut - Δ(u - 1)+ = 0, in D'(Rn x (0,T)),for T > 0, n ≥ 1. Equation (0.1) is a formulation of a one-phase Stefan problem: in this connection u is the enthalpy, (u - 1)+ the temperature, and u = 1 the critical temperature of change of phase. Our estimate may be written in the form(0.2) ∫Rn u(x,t) e-|x|2 / (2 (T - t)) dx ≤ C, 0 <...
Initial Value Problems in Lp for Systems with Variable Coefficients.
Initial-boundary value problem with a nonlocal condition for a viscosity equation.
Initial-boundary value problems describing mobile carrier transport in semiconductor devices
Innere Abschätzungen für Lösungen nichtlinearer elliptischer Differentialgleichungen zweiter Ordnung in n Variablen.
Instabilities in a reaction diffusion model: spatially homogeneous and distributed systems.
Instability in semi-infinite strips of solutions of linear systems.
The present paper is devoted to study the behaviour at infinity of some solutions of non autonomous and non homogeneous second order linear systems in semi-infinite strips.
Instability of mixed finite elements for Richards' equation
Richards' equation is a widely used model of partially saturated flow in a porous medium. In order to obtain conservative velocity field several authors proposed to use mixed or mixed-hybrid schemes to solve the equation. In this paper, we shall analyze the mixed scheme on 1D domain and we show that it violates the discrete maximum principle which leads to catastrophic oscillations in the solution.
Instability of oscillations in cable-stayed bridges
In this paper the stability of two basic types of cable stayed bridges, suspended by one or two rows of cables, is studied. Two linearized models of the center span describing the vertical and torsional oscillations are investigated. After the analysis of these models, a stability criterion is formulated. The criterion expresses a relation between the eigenvalues of the vertical and torsional oscillations of the center span. The continuous dependence of the eigenvalues on some data is studied and...
Instability of radial standing waves of Schrödinger equation on the exterior of a ball.