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Nonlinear Functional Analysis and Applications
Nonlinear functional analysis is a central subject of mathematics with applications in many areas of geometry, analysis, fl uid and elastic mechanics, physics, chemistry, biology, control theory, optimization, game theory, economics etc. This work is devoted, in a self-contained way, to several subjects of this topic such as theory of accretive operators in Banach spaces, theory of abstract Cauchy problem, metric and topological fixed point theory. Special emphasis is given to the study how these theories can be used to obtain existence and uniqueness of solutions for several types of evolution and stationary equations. In particular, equations arising in dynamical population and neutron transport equations are discussed.
Shape Optimization
This book investigates how domain dependent quantities from geometry and physics behave when the domain is perturbed. Of particular interest are volume- and perimeter-preserving perturbations. The first and second derivatives with respect to the perturbation are exploited for domain functionals like eigenvalues, energies and geometrical quantities. They provide necessary conditions for optimal domains and are useful when global approaches like symmetrizations fail. The book is exampledriven and illustrates the usefulness of domain variations in various applications.
Elliptic and Parabolic Equations Involving the Hardy-Leray Potential
The scientific literature on the Hardy-Leray inequality, also known as the uncertainty principle, is very extensive and scattered. The Hardy-Leray potential shows an extreme spectral behavior and a peculiar influence on diffusion problems, both stationary and evolutionary. In this book, a big part of the scattered knowledge about these different behaviors is collected in a unified and comprehensive presentation.
Lie Group Analysis of Differential Equations
The book is focused on physical interpretation and visualization of the obtained invariant solutions for nonlinear mathematical modeling of atmospheric and ocean waves. This volume represents a unique blend of analytical and numerical methods complemented by the author's developments in ocean and atmospheric sciences and it is meant for researchers and graduate students interested in applied mathematics and mathematical modeling.
Hardy Inequalities and Applications
This book derives new Hardy inequalities with double singular weights - at an interior point and on the boundary of the domain. We focus on the optimality of Hardy constant and on its attainability. Applications include: results about existence\nonexistence and controllability for parabolic equations with double singular potentials; estimates from below of the fi rst eigenvalue of p-Laplacian with Dirichlet boundary conditions.
Nonautonomous Fractional Evolution Equations
Fractional evolution equations describe various complex and nonlocal systems with memory. This volume investigates fractional evolution equations, in infinite intervals. The book covers a range of topics, including the existence, uniqueness, attractivity, and applications to fractional diffusion equations and fractional Schrodinger equations. Researchers and graduate students in pure and applied mathematics will find this a useful reference.
Mathematical Reviews
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Elliptic and Parabolic Equations Involving the Hardy-Leray Potential
The scientific literature on the Hardy-Leray inequality, also known as the uncertainty principle, is very extensive and scattered. The Hardy-Leray potential shows an extreme spectral behavior and a peculiar influence on diffusion problems, both stationary and evolutionary. In this book, a big part of the scattered knowledge about these different behaviors is collected in a unified and comprehensive presentation.
Heritage Quest
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