A blow up condition for a nonautonomous semilinear system.
A blowup analysis of the mean field equation for arbitrarily signed vortices
We study the noncompact solution sequences to the mean field equation for arbitrarily signed vortices and observe the quantization of the mass of concentration, using the rescaling argument.
A blow-up mechanism for a chemotaxis model
A blow-up result for nonlinear diffusion equations
A Boundary Value Problem Connected with Response of Semi-space to a Short Laser Pulse
In this paper a mixed boundary value problem for the fourth order hyperbolic equation with constant coefficients which is connected with response of semi-space to a short laser pulse» and belongs to generalized Thermoelasticity is studied. This problem was considered by R. B. Hetnarski and J. Ignaczak, who established some important physical consequences. The present paper contains proof of the existence, uniqueness and continuous dependence of a solution on the datum, together with an effective...
A brief introduction to homogenization and miscellaneous applications*
This paper is a set of lecture notes for a short introductory course on homogenization. It covers the basic tools of periodic homogenization (two-scale asymptotic expansions, the oscillating test function method and two-scale convergence) and briefly describes the main results of the more general theory of G− or H−convergence. Several applications of the method are given: derivation of Darcy’s law for flows in porous media, derivation of the porosity...
A capacity method for the study of Dirichlet problems for elliptic systems in varying domains
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 nonlinear conservative elliptic equations in cylinders
A combustion model with unbounded thermal conductivity and reactant diffusivity in non-smooth domains.
A Commuting Vectorfields Approach to Strichartz type Inequalities and Applications to Quasilinear Wave Equations
A Construction of Stable Subharmonic Orbits in Monotone Time-periodic Dynamical Systems.
A decay estimate for a class of hyperbolic pseudo-differential equations
We consider the equation , where is a first order pseudo-differential operator with real symbol . Under a suitable convexity assumption on we find the decay properties for . These can be applied to the linear Maxwell system in anisotropic media and to the nonlinear Cauchy Problem , . If is a smooth function which satisfies near , and is small in suitably Sobolev norm, we prove global existence theorems provided is greater than a critical exponent.
A description of blow-up for the solid fuel ignition model
A description of self-similar blow-up for dimensions
A diffusion equation for composite materials.
A discrete phenomenon in propagation of singularities
A Gamma-convergence argument for the blow-up of a non-local semilinear parabolic equation with Neumann boundary conditions
A general decay estimate for a finite memory thermoelastic Bresse system
This work considers a Bresse system with viscoelastic damping on the vertical displacement and heat conduction effect on the shear angle displacement. A general stability result with minimal condition on the relaxation function is obtained. The system under investigation, to the best of our knowledge, is new and has not been studied before in the literature. What is more interesting is the fact that our result holds without the imposition of the equal speed of wave propagation condition, and differentiation...