Improved theory for a nonlinear degenerate parabolic equation
Inégalités différentielles fonctionnelles du type elliptique
Inégalités isopérimétriques et applications. Domaines nodaux des fonctions propres
Initial limits of temperatures on arbitrary open sets.
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...
Instantaneous blow-up of solutions to a class of hyperbolic inequalities.
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.
Interior Hölder estimates for solutions of Schrödinger equations and the regularity of nodal sets
Invariant regions and global existence of solutions for reaction-diffusion systems with a tridiagonal matrix of diffusion coefficients and nonhomogeneous boundary conditions.
Isolatedness of characteristic points at blow-up for a semilinear wave equation in one space dimension
We consider the semilinear wave equation with power nonlinearity in one space dimension. We first show the existence of a blow-up solution with a characteristic point. Then, we consider an arbitrary blow-up solution , the graph of its blow-up points and the set of all characteristic points and show that is locally finite. Finally, given , we show that in selfsimilar variables, the solution decomposes into a decoupled sum of (at least two) solitons, with alternate signs and that forms a...