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This volume gathers contributions in the field of partial
differential equations, with a focus on mathematical models in
phase transitions, complex fluids and thermomechanics. These
contributions are dedicated to Professor Gianni Gilardi on the
occasion of his 70th birthday. It particularly develops the
following thematic areas: nonlinear dynamic and stationary
equations; well-posedness of initial and boundary value problems
for systems of PDEs; regularity properties for the solutions;
optimal control problems and optimality conditions; feedback
stabilization and stability results. Most of the articles are
presented in a self-contained manner, and describe new achievements
and/or the state of the art in their line of research, providing
interested readers with an overview of recent advances and future
research directions in PDEs.
This book, based on a selection of talks given at a dedicated
meeting in Cortona, Italy, in June 2013, shows the high degree of
interaction between a number of fields related to applied sciences.
Applied sciences consider situations in which the evolution of a
given system over time is observed, and the related models can be
formulated in terms of evolution equations (EEs). These equations
have been studied intensively in theoretical research and are the
source of an enormous number of applications. In this volume,
particular attention is given to direct, inverse and control
problems for EEs. The book provides an updated overview of the
field, revealing its richness and vitality.
This work presents a detailed study of linear abstract degenerate
differential equations, using both the semigroups generated by
multivalued (linear) operators and extensions of the operational
method from Da Prato and Grisvard. The authors describe the recent
and original results on PDEs and algebraic-differential equations,
and establishes the analyzability of the semigroup generated by
some degenerate parabolic operators in spaces of continuous
functions.
This volume gathers contributions in the field of partial
differential equations, with a focus on mathematical models in
phase transitions, complex fluids and thermomechanics. These
contributions are dedicated to Professor Gianni Gilardi on the
occasion of his 70th birthday. It particularly develops the
following thematic areas: nonlinear dynamic and stationary
equations; well-posedness of initial and boundary value problems
for systems of PDEs; regularity properties for the solutions;
optimal control problems and optimality conditions; feedback
stabilization and stability results. Most of the articles are
presented in a self-contained manner, and describe new achievements
and/or the state of the art in their line of research, providing
interested readers with an overview of recent advances and future
research directions in PDEs.
This book, based on a selection of talks given at a dedicated
meeting in Cortona, Italy, in June 2013, shows the high degree of
interaction between a number of fields related to applied sciences.
Applied sciences consider situations in which the evolution of a
given system over time is observed, and the related models can be
formulated in terms of evolution equations (EEs). These equations
have been studied intensively in theoretical research and are the
source of an enormous number of applications. In this volume,
particular attention is given to direct, inverse and control
problems for EEs. The book provides an updated overview of the
field, revealing its richness and vitality.
The aim of these notes is to include in a uniform presentation
style several topics related to the theory of degenerate nonlinear
diffusion equations, treated in the mathematical framework of
evolution equations with multivalued m-accretive operators in
Hilbert spaces. The problems concern nonlinear parabolic equations
involving two cases of degeneracy. More precisely, one case is due
to the vanishing of the time derivative coefficient and the other
is provided by the vanishing of the diffusion coefficient on
subsets of positive measure of the domain. From the mathematical
point of view the results presented in these notes can be
considered as general results in the theory of degenerate nonlinear
diffusion equations. However, this work does not seek to present an
exhaustive study of degenerate diffusion equations, but rather to
emphasize some rigorous and efficient techniques for approaching
various problems involving degenerate nonlinear diffusion
equations, such as well-posedness, periodic solutions, asymptotic
behaviour, discretization schemes, coefficient identification, and
to introduce relevant solving methods for each of them.
With contributions from some of the leading authorities in the
field, the work in Differential Equations: Inverse and Direct
Problems stimulates the preparation of new research results and
offers exciting possibilities not only in the future of mathematics
but also in physics, engineering, superconductivity in special
materials, and other scientific fields. Exploring the hypotheses
and numerical approaches that relate to pure and applied
mathematics, this collection of research papers and surveys extends
the theories and methods of differential equations. The book begins
with discussions on Banach spaces, linear and nonlinear theory of
semigroups, integrodifferential equations, the physical
interpretation of general Wentzell boundary conditions, and
unconditional martingale difference (UMD) spaces. It then proceeds
to deal with models in superconductivity, hyperbolic partial
differential equations (PDEs), blowup of solutions,
reaction-diffusion equation with memory, and Navier-Stokes
equations. The volume concludes with analyses on Fourier-Laplace
multipliers, gradient estimates for Dirichlet parabolic problems, a
nonlinear system of PDEs, and the complex Ginzburg-Landau equation.
By combining direct and inverse problems into one book, this
compilation is a useful reference for those working in the world of
pure or applied mathematics.
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