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Here, the authors present modern methods of analysis for nonlinear
systems which may occur in fields such as physics, chemistry,
biology, or economics. They concentrate on the following topics,
specific for such systems: (a) constructive existence results and
regularity theorems for all weak solutions; (b) convergence results
for solutions and their approximations; (c) uniform global behavior
of solutions in time; and (d) pointwise behavior of solutions for
autonomous problems with possible gaps by the phase variables. The
general methodology for the investigation of dissipative dynamical
systems with several applications including nonlinear parabolic
equations of divergent form, nonlinear stochastic equations of
parabolic type, unilateral problems, nonlinear PDEs on Riemannian
manifolds with or without boundary, contact problems as well as
particular examples is established. As such, the book is addressed
to a wide circle of mathematical, mechanical and engineering
readers.
Here, the authors present modern methods of analysis for nonlinear
systems which may occur in fields such as physics, chemistry,
biology, or economics. They concentrate on the following topics,
specific for such systems: (a) constructive existence results and
regularity theorems for all weak solutions; (b) convergence results
for solutions and their approximations; (c) uniform global behavior
of solutions in time; and (d) pointwise behavior of solutions for
autonomous problems with possible gaps by the phase variables. The
general methodology for the investigation of dissipative dynamical
systems with several applications including nonlinear parabolic
equations of divergent form, nonlinear stochastic equations of
parabolic type, unilateral problems, nonlinear PDEs on Riemannian
manifolds with or without boundary, contact problems as well as
particular examples is established. As such, the book is addressed
to a wide circle of mathematical, mechanical and engineering
readers.
Here, the authors present modern mathematical methods to solve
problems of differential-operator inclusions and evolution
variation inequalities which may occur in fields such as
geophysics, aerohydrodynamics, or fluid dynamics. For the first
time, they describe the detailed generalization of various
approaches to the analysis of fundamentally nonlinear models and
provide a toolbox of mathematical equations. These new mathematical
methods can be applied to a broad spectrum of problems. Examples of
these are phase changes, diffusion of electromagnetic, acoustic,
vibro-, hydro- and seismoacoustic waves, or quantum mechanical
effects. This is the second of two volumes dealing with the
subject.
Here, the authors present modern mathematical methods to solve
problems of differential-operator inclusions and evolution
variation inequalities which may occur in fields such as
geophysics, aerohydrodynamics, or fluid dynamics. For the first
time, they describe the detailed generalization of various
approaches to the analysis of fundamentally nonlinear models and
provide a toolbox of mathematical equations. These new mathematical
methods can be applied to a broad spectrum of problems. Examples of
these are phase changes, diffusion of electromagnetic, acoustic,
vibro-, hydro- and seismoacoustic waves, or quantum mechanical
effects. This is the first of two volumes dealing with the subject.
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