Analysis of the Energy Decay of a Degenerated Thermoelasticity System

In this paper, we study a system of thermoelasticity with a degenerated second order operator in the Heat equation. We analyze the evolution of the energy density of a family of solutions. We consider two cases: when the set of points where the ellipticity of the Heat operator fails is included in a hypersurface and when it is an open set. In the first case and under special assumptions, we prove that the evolution of the energy density is the one of a damped wave equation: propagation along the rays of geometric optic and damping according to a microlocal process. In the second case, we show that the energy density propagates along rays which are distortions of the rays of geometric optic.Comment: 28 page

Singular limits for 4-dimensional semilinear elliptic problems with exponential nonlinearity

Using some nonlinear domain decomposition method, we prove the existence of singular limits for solution of semilinear elliptic problems with exponential nonlinearity.Comment: 29 page

Multiplicity results for elliptic Kirchhoff-type problems

Abstract The aim of this paper is to establish the existence of multiple solutions for a perturbed Kirchhoff-type problem depending on two real parameters. More precisely, we show that an appropriate oscillating behaviour of the nonlinear part, even under small perturbations, ensures the existence of at least three nontrivial weak solutions. Our approach combines variational methods with properties of nonlocal fractional operators

The Land Revenue History of the Rajshahi Zamindari, (1765-1793).

This work is devoted to a study of the land revenue history of the Rajshahi Zamindari from 1765 to 1793. The first chapter is introductory and narrates the creation of this vast zamindari in the first half of the eighteenth century. The second chapter deals with the seven years of Diwani rule in Bengal from 1765 to 1772, years of hesitation and confusion, and discusses the East India Company's early revenue policies and their implementation in Rajshahi. The arguments of James Grant about the proper level of demand upon Rajshahi, and the results of collection by the Supervisor and under the Triennial settlement are reviewed, and the results of the 1770 famine are assessed. The third chapter discusses the Quinquennial farming settlement introduced by Warren Hastings in 1772, and the attempts made by Rani Bhabani, zamindar of Rajshahi to work with and then to resist the Company. Particular attention is paid to the fate of the zamindari during the conflict in the Calcutta Council between Hastings and Barwell, and Clavering, Monson and Francis. The fourth chapter reviews the working of the temporary settlement of Rajshahi under the Collectors William Hosea and Edward Baber, acting through local agents, and the causes of failure which led to a renewed settlement with the zamindar. The fifth chant 'Jr is devoted to Hastings' Permanent Plan for the Revenue Administration of 1781, and to his refusal to allow any settlement with the Rani. The four different revenue experiments in Rajshahi which thereupon follow are then considered, and the circumstances of their success or failure. The last chapter studies the changes in attitude in India and England which led to the adoption of a permanent zarlindari settlement in Bengal, and surveys the difficulties which precede Rajshahi's ultimate inclusion in that settlement

Construction of singular limits for four-dimensional elliptic problems with exponentially dominated nonlinearity

AbstractThe authors consider the existence of singular limit solution for a family of nonlinear elliptic problems with exponentially dominated nonlinearity and Navier boundary condition

Singular limits for the bi-laplacian operator with exponential nonlinearity in R4\R^4

Let $\Omega$ be a bounded smooth domain in $\mathbb{R}^{4}$ such that for some integer $d\geq1$ its $d$-th singular cohomology group with coefficients in some field is not zero, then problem {\Delta^{2}u-\rho^{4}k(x)e^{u}=0 & \hbox{in}\Omega, u=\Delta u=0 & \hbox{on}\partial\Omega, has a solution blowing-up, as $\rho\to0$, at $m$ points of $\Omega$, for any given number $m$.Comment: 30 pages, to appear in Ann. IHP Non Linear Analysi

Existence of Multistring Solutions of the Self-Gravitating Massive W−W-Boson

We consider a semilinear elliptic system which include the model system of the $W-$strings in the cosmology as a special case. We prove existence of multi-string solutions and obtain precise asymptotic decay estimates near infinity for the solutions. As a special case of this result we solve an open problem posed in \cite{yan}Comment: 12 page