The -Laplacian – mascot of nonlinear analysis
The version of mixed finite element methods for parabolic problems
The -version of the finite element method for elliptic equations of order
The Painlevé III equation and the Iwasawa decomposition.
The Painlevé test and reducibility to the canonical forms for higher-dimensional soliton equations with variable-coefficients.
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 parabolic equations as a limiting case of hyperbolic and elliptic equations
The parabolic mixed Cauchy-Dirichlet problem in spaces of functions which are hölder continuous with respect to space variables
We give a new proof, based on analytic semigroup methods, of a maximal regularity result concerning the classical Cauchy-Dirichlet's boundary value problem for second order parabolic equations. More specifically, we find necessary and sufficient conditions on the data in order to have a strict solution which is bounded with values in (0 < < 1), with bounded with values in .
The parametrix of regular hypoelliptic boundary value problems
The PDE describing constant mean curvature surfaces
We give an expository account of a Weierstrass type representation of the non-zero constant mean curvature surfaces in space and discuss the meaning of the representation from the point of view of partial differential equations.
The penalty method for the equations of viscoelastic media
The Penetrable sphere with a soft Eccentric core within an Accoustic wave field
The periodic boundary value problem for some second order ordinary differential equations
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 pertubatively stable spectrum of a periodic Schrödinger operator.
The p-harmonic system with measure-valued right hand side
The phase field equations and gradient flows of marginal functions.
The phase space of one generalized model by Oskolkov.