Singular functional differential equations of neutral type in Banach spaces

AbstractThe well-posedness of a large class of singular partial differential equations of neutral type is discussed. Here the term singularity means that the difference operator of such equations is nonatomic at zero. This fact offers many difficulties in applying the usual methods of perturbation theory and Laplace transform technique and thus makes the study interesting. Our approach is new and it is based on functional analysis of semigroup of operators in an essential way, and allows us to introduce a new concept of solutions for such equations. Finally, we study the well-posedness of a singular reaction–diffusion equation of neutral type in weighted Lebesgue's spaces

The Irony of Secession

The election of Abraham Lincoln to the presidency of the United States marked the beginning of active measures for separation in the state of Florida. Throughout the state mass meetings were held to protest the ascendancy of “Black Republicanism.” The term “secession” so truculently advanced by a militant minority since the Compromise of 1850 began to be advanced by an ever increasing number of Floridians inflamed by the spirit of the time

Unbounded Perturbations of the Generator Domain

Let X, U and Z be Banach spaces such that Z in X (with continuous and dense embedding), L : Z ->X be a closed linear operator and consider closed linear operators G, M : Z -> U. Putting conditions on G and M we show that the operator A = L with domain D(A) ={z∈Z: Gz=Mz} generates a C0- semigroup on X. Moreover, we give a variation of constants formula for the solution of an inhomogeneous problem. Several examples will be given, in particular heat equation with distributed unbounded delay at the boundary condition

Genetics and the (social) body testing for the cystic fibrosis gene

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal