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Evolution Equations of von Karman Type (Paperback, 1st ed. 2015)
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Evolution Equations of von Karman Type (Paperback, 1st ed. 2015)
Series: Lecture Notes of the Unione Matematica Italiana, 17
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In these notes we consider two kinds of nonlinear evolution
problems of von Karman type on Euclidean spaces of arbitrary even
dimension. Each of these problems consists of a system that results
from the coupling of two highly nonlinear partial differential
equations, one hyperbolic or parabolic and the other elliptic.
These systems take their name from a formal analogy with the von
Karman equations in the theory of elasticity in two dimensional
space. We establish local (respectively global) results for strong
(resp., weak) solutions of these problems and corresponding
well-posedness results in the Hadamard sense. Results are found by
obtaining regularity estimates on solutions which are limits of a
suitable Galerkin approximation scheme. The book is intended as a
pedagogical introduction to a number of meaningful application of
classical methods in nonlinear Partial Differential Equations of
Evolution. The material is self-contained and most proofs are given
in full detail. The interested reader will gain a deeper insight
into the power of nontrivial a priori estimate methods in the
qualitative study of nonlinear differential equations.
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