Publications of Morosanu, Gheorghe

Elliptic-like regularization of semilinear evolution equations

Consider in a real Hilbert space the Cauchy problem (P0): u′(t)+Au(t)+Bu(t) = f (t), 0 ≤ t ≤ T ; u(0) = u_0, where −A is the generator of a C_0-semigroup of linear contractions and B is a smooth nonlinear operator. We associate with (P_0) the following problem: (Pε): −εu′′(t) + u′(t) + Au(t) + Bu(t) = f (t), 0 ≤ t ≤ T ; u(0) = u_0, u(T ) = u_1, where ε > 0 is a small parameter. Existence, uniqueness and higher regularity for both (P0) and (Pε) are investigated and an asymptotic expansion for the solution of problem (Pε) is established, showing the presence of a boundary layer near t = T .

On the method of alternating resolvents

The work of H. Hundal (Nonlinear Anal. 57 (2004), 35-61) has revealed that the sequence generated by the method of alternating projections converges weakly, but not strongly in general. This paper seeks to design strongly convergent algorithms by means of alternating the resolvents of two maximal monotone operators, A and B, that can be used to approximate common zeroes of A and B. In particular, methods of alternating projections which generate sequences that converge strongly are obtained. A particular case of such algorithms enables one to approximate minimum values of certain convex functionals under less restrictive conditions on the regularization parameters involved.

Existence and multiplicity of solutions for an anisotropic elliptic problem involving variable exponent growth conditions

We study a boundary value problem of the type in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in (N≥ 3) with smooth boundary and the functions are of the type with , (i = 1, …, N). Combining the mountain pass theorem of Ambrosetti and Rabinowitz and Ekeland's variational principle we show that under suitable conditions the problem has two non-trivial weak solutions.

On a class of boundary value problems involving the p-biharmonic operator

A nonlinear boundary value problem involving the p-biharmonic operator is investigated, where p > 1. It describes various problems in the theory of elasticity, e.g., the shape of an elastic beam where the bending moment depends on the curvature as a power function with exponent p − 1. We prove existence of solutions satisfying a quite general boundary condition that incorporates many particular boundary conditions which are frequently considered in the literature.

A necessary and sufficient condition for input identifiability for linear time-invariant systems

A necessary and sufficient condition for input identifiability for linear autonomous systems is given. The result is based on a finite iterative process and its proof relies on elementary arguments involving matrices, finite dimensional linear spaces, Gronwall’s lemma, and linear differential systems. Our condition is equivalent to the classical condition involving the geometrical concept of controlled invariant [V. Basile, G. Marro, Controlled and Conditioned Invariants in Linear System Theory, Prentice Hall, Englewood Cliffs, NJ, 1992, p. 237] and the dimension reduction algorithm that we propose seems to be useful in designing deconvolution methods.

An extension of the Jordan-von Neumann theorem

The purpose of this Note is to present an extension of the classical Jordan-von Neumann (JN) theorem [3] - which is recalled below - to the case of a normed space over the skew field IH of quaternions. It is known that this extension is valid in a more general framework (see [5], [6], [7], [8]), but our approach is based on elementary arguments only. So, this result may be of interest for students, applied researchers, etc. We think this extension could be applied to control theory, mechanics and other areas.