The Oblique Derivative Problem. I.
The oscillatory behavior of second order nonlinear elliptic equations.
The -Laplace eigenvalue problem as in a Finsler metric
We consider the -Laplacian operator on a domain equipped with a Finsler metric. We recall relevant properties of its first eigenfunction for finite and investigate the limit problem as .
The -Laplacian in domains with small random holes
{ll -div (|Duh|p-2 Duh)=g, & in D Eh uhH1,p0(D Eh). . where and are random subsets of a bounded open set of . By...
The parabolic Anderson model in a dynamic random environment: Basic properties of the quenched Lyapunov exponent
In this paper we study the parabolic Anderson equation , , , where the -field and the -field are -valued, is the diffusion constant, and is the discrete Laplacian. The -field plays the role of adynamic random environmentthat drives the equation. The initial condition , , is taken to be non-negative and bounded. The solution of the parabolic Anderson equation describes the evolution of a field of particles performing independent simple random walks with binary branching: particles jump...
The periodic parabolic eigenvalue problem with L... weight.
The periodic unfolding method for a class of parabolic problems with imperfect interfaces
In this paper, we use the adapted periodic unfolding method to study the homogenization and corrector problems for the parabolic problem in a two-component composite with ε-periodic connected inclusions. The condition imposed on the interface is that the jump of the solution is proportional to the conormal derivative via a function of order εγ with γ ≤ −1. We give the homogenization results which include those obtained by Jose in [Rev. Roum. Math. Pures Appl. 54 (2009) 189–222]. We also get the...
The periodic unfolding method in perforated domains.
The Picard-Ionescu problem for hyperbolic inclusions with modified argument
We consider the Picard-Ionescu problem for hyperbolic inclusions with modified argument. Existence of a local solution is proved and some properties of the set of solutions are established.
The porous medium equation as a finite-speed approximation to a Hamilton-Jacobi equation
The positive radial solutions of a class of semilinear elliptic equations.
The preventive effect of the convection and of the diffusion in the blow-up phenomenon for parabolic equations
The problems of blow-up for nonlinear heat equations. Complete blow-up and avalanche formation
We review the main mathematical questions posed in blow-up problems for reaction-diffusion equations and discuss results of the author and collaborators on the subjects of continuation of solutions after blow-up, existence of transient blow-up solutions (so-called peaking solutions) and avalanche formation as a mechanism of complete blow-up.
The Propagation of Singularities along Gliding Rays.
The propagation of singularities for pseudo-differential operators with self-tangential characteristics
The pseudo--Laplace eigenvalue problem and viscosity solutions as
We consider the pseudo--laplacian, an anisotropic version of the -laplacian operator for . We study relevant properties of its first eigenfunction for finite and the limit problem as .
The pseudo-p-Laplace eigenvalue problem and viscosity solutions as p → ∞
We consider the pseudo-p-Laplacian, an anisotropic version of the p-Laplacian operator for . We study relevant properties of its first eigenfunction for finite p and the limit problem as p → ∞.
The pullback attractors for the nonautonomous Camassa-Holm equations.
The quasineutral limit problem in semiconductors sciences
The mathematical analysis on various mathematical models arisen in semiconductor science has attracted a lot of attention in both applied mathematics and semiconductor physics. It is important to understand the relations between the various models which are different kind of nonlinear system of P.D.Es. The emphasis of this paper is on the relation between the drift-diffusion model and the diffusion equation. This is given by a quasineutral limit from the DD model to the diffusion equation.
The regularity of weak and very weak solutions of the Poisson equation on polygonal domains with mixed boundary conditions (part II)
We examine the regularity of weak and very weak solutions of the Poisson equation on polygonal domains with data in L². We consider mixed Dirichlet, Neumann and Robin boundary conditions. We also describe the singular part of weak and very weak solutions.