the theory of stability of ordinary differential equations contains the germs for a theory of stability of nonlinear evolution semigroups... This book is devoted to a self-contained systematic exposition of these matters and incorporates many of the author's own substantial results in the field.
This book has been followed by a series of related papers, including his articles on second-order evolution equations governed by monotone operators. These publications provide a complete answer to the long-standing existence question in the non-homogeneous case. Both his joint monograph on functional methods and that on singular perturbations contain original material mostly due to the authors, bringing new ideas and methods that are useful in exploring mathematical models described by linear and nonlinear differential equations. In particular the book on singular perturbations combines results from different parts of mathematics to offer a detailed asymptotic analysis of some important classes of singularly perturbed boundary value problems which are mathematical models for various phenomena in biology, chemistry, engineering. This book has been followed by some related joint papers on abstract semilinear and fully nonlinear evolution equations with significant applications. Moroșanu has also works in Calculus of Variations, Fluid Mechanics, etc. More specifically, his legacy of contributions concerns the following topics: • first and second-order evolution equations in Hilbert spaces; • initial-boundary value problems for parabolic and hyperbolic partial differential equations and systems ; • singular perturbation theory for nonlinear partial differential equations and semilinear evolution equations in Hilbert spaces; • boundary value problems for elliptic equations, including equations involving p-Laplacians, related eigenvalue problems; • nonlinear ordinary differential equations, integro-differential equations, delay differential equations, equations involving ordinary p-Laplacians; • monotone operators, nonlinear differential operators; • difference equations in Hilbert spaces, including proximal point algorithms; • the Fourier method for solving abstract evolution equations; • optimization, input identifiability, optimal control; • applications in acoustics, capillarity theory, diffusion processes, fluid flows, hydraulics, integrated circuits, mathematical biology and ecology, nonlinear oscillators, phase field equations, self-organized systems, telegraph systems, etc. In 1983 he was awarded the Gheorghe Lazăr Prize of the Romanian Academy in recognition of his outstanding contributions to the theory of hyperbolic partial differential equations. He holds honorary doctorates from the University of Craiova, Craiova, Romania and from Ovidius University, Constanța, Romania. In 2019, he received the title of Professor Honoris Causa from the Babeș-Bolyai University, Cluj-Napoca, Romania A school Moroșanu himself attended between 1957 and 1965 has been named after him since 2007, when he also received the title of honorary citizen of Darabani in recognition of his accomplishments.
