On the Cauchy problem of a quasilinear degenerate parabolic equation.
On the Chaplighin method for partial differential equations of the first order
On the Charney Conjecture of Data Assimilation Employing Temperature Measurements Alone: The Paradigm of 3D Planetary Geostrophic Model
Analyzing the validity and success of a data assimilation algorithmwhen some state variable observations are not available is an important problem in meteorology and engineering. We present an improved data assimilation algorithm for recovering the exact full reference solution (i.e. the velocity and temperature) of the 3D Planetary Geostrophic model, at an exponential rate in time, by employing coarse spatial mesh observations of the temperature alone. This provides, in the case of this paradigm,...
On the coincidence set in biharmonic variational inequalities with thin obstacles
On the collision of two solitons for the generalized KdV equation in the nonintegrable case
On the complex structure of positive solutions to Matukuma-type equations
On the concentration of solutions of singularly perturbed Hamiltonian systems in .
On the continuation of solutions for elliptic equations in two variables
On the continuity of degenerate n-harmonic functions
We study the regularity of finite energy solutions to degenerate n-harmonic equations. The function K(x), which measures the degeneracy, is assumed to be subexponentially integrable, i.e. it verifies the condition exp(P(K)) ∈ Lloc1. The function P(t) is increasing on [0,∞[ and satisfies the divergence condition∫ 1 ∞ P ( t ) t 2 d t = ∞ .
On the continuity of degenerate n-harmonic functions
We study the regularity of finite energy solutions to degenerate n-harmonic equations. The function K(x), which measures the degeneracy, is assumed to be subexponentially integrable, i.e. it verifies the condition exp(P(K)) ∈ Lloc1. The function P(t) is increasing on [0,∞[ and satisfies the divergence condition
On the Convective Cahn-Hilliard Equation
The author studies the convective Cahn-Hilliard equation. Some results on the existence of classical solutions and asymptotic behavior of solutions are established. The instability of the traveling waves is also discussed.
On the cost of null-control of an artificial advection-diffusion problem
In this paper we study the null-controllability of an artificial advection-diffusion system in dimension n. Using a spectral method, we prove that the control cost goes to zero exponentially when the viscosity vanishes and the control time is large enough. On the other hand, we prove that the control cost tends to infinity exponentially when the viscosity vanishes and the control time is small enough.
On the critical Neumann problem with lower order perturbations
We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent and lower order perturbations in bounded domains. Solutions are obtained by min max methods based on a topological linking. A nonlinear perturbation of a lower order is allowed to interfere with the spectrum of the operator -Δ with the Neumann boundary conditions.
On the decay estimates for the wave equation with a local degenerate or nondegenerate dissipation.
On the Decay of Solutions of Some Nonlinear Dissipative Wave Equations in Higher Dimensions.
On the decay of the solutions of some nonlinear Schrödinger equations
On the definition and properties of p-superharmonic functions.
On the definition of the SUPG parameter.
On the density of the range for some nonlinear operators
On the differentiability of solutions of quasilinear elliptic equations