-total stability and almost periodicity for some partial functional differential equations with infinite delay.
2D-1D dimensional reduction in a toy model for magnetoelastic interactions
The paper deals with the dimensional reduction from 2D to 1D in magnetoelastic interactions. We adopt a simplified, but nontrivial model described by the Landau-Lifshitz-Gilbert equation for the magnetization field coupled to an evolution equation for the displacement. We identify the limit problem by using the so-called energy method.
5-Shaped Bifurcation Curves of Nonlinear Elliptic Boundary Value Problems.
"Best possible'' maximum principles
“Farfield” behavior of solutions to partial differential equations : asymptotic expansions and maximal rates of decay along a ray
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-convergence of concentration problems
In this paper, we use -convergence techniques to study the following variational problemwhere , with , and is a bounded domain of , . We obtain a -convergence result, on which one can easily read the usual concentration phenomena arising in critical growth problems. We extend the result to a non-homogeneous version of problem . Finally, a second order expansion in -convergence permits to identify the concentration points of the maximizing sequences, also in some non-homogeneous case.
Γ-convergence approach to variational problems in perforated domains with Fourier boundary conditions
The work focuses on the Γ-convergence problem and the convergence of minimizers for a functional defined in a periodic perforated medium and combining the bulk (volume distributed) energy and the surface energy distributed on the perforation boundary. It is assumed that the mean value of surface energy at each level set of test function is equal to zero. Under natural coercivity and p-growth assumptions on the bulk energy, and the assumption that the surface energy satisfies p-growth upper bound,...
Γ-convergence of functionals on divergence-free fields
We study the stability of a sequence of integral functionals on divergence-free matrix valued fields following the direct methods of Γ-convergence. We prove that the Γ-limit is an integral functional on divergence-free matrix valued fields. Moreover, we show that the Γ-limit is also stable under volume constraint and various type of boundary conditions.
-устойчивость классов отображений и системы линейных уравнений с частными производными.
-convergence.
-convergence of nonlinear monotone operators in perforated domains with holes of small size
This paper is devoted to the homogenization beyond the periodic setting, of nonlinear monotone operators in a domain in with isolated holes of size ( a small parameter). The order of the size of the holes is twice that of the oscillations of the coefficients of the operator, so that the problem under consideration is a reiterated homogenization problem in perforated domains. The usual periodic perforation of the domain and the classical periodicity hypothesis on the coefficients of the operator...
Алгебры Ли и лаксовы уравнения со спектральным параметром на эллиптической кривой
Анализ режимов с обострением в задаче о термисторе.
Аналитические первые интегралы нелинейных параболических уравнений и их приложения
Аналитическое продолжение решений однородных неправильно эллиптических уравнений высшего порядка на плоскости.
Аналитичность и теоремы типа Лиувилля и Фрагмена - Линделёфа для общих эллиптических систем дифференциальных уравнений
Аналитичность решений сингулярных эллиптических уравнений