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Analytic Semigroups and Optimal Regularity in Parabolic Problems (Paperback, Softcover reprint of the original 1st ed. 1995)
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Analytic Semigroups and Optimal Regularity in Parabolic Problems (Paperback, Softcover reprint of the original 1st ed. 1995)
Series: Progress in Nonlinear Differential Equations and Their Applications, 16
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Total price: R3,092
Discovery Miles: 30 920
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This book gives a systematic treatment of the basic theory of
analytic semigroups and abstract parabolic equations in general
Banach spaces, and of how such a theory may be used in parabolic
PDE's. It takes into account the developments of the theory during
the last fifteen years, and it is focused on classical solutions,
with continuous or Holder continuous derivatives. On one hand,
working in spaces of continuous functions rather than in Lebesgue
spaces seems to be appropriate in view of the number of parabolic
problems arising in applied mathematics, where continuity has
physical meaning; on the other hand it allows one to consider any
type of nonlinearities (even of nonlocal type), even involving the
highest order derivatives of the solution, avoiding the limitations
on the growth of the nonlinear terms required by the LP approach.
Moreover, the continuous space theory is, at present, sufficiently
well established. For the Hilbert space approach we refer to J. L.
LIONS - E. MAGENES [128], M. S. AGRANOVICH - M. l. VISHIK [14], and
for the LP approach to V. A. SOLONNIKOV [184], P. GRISVARD [94], G.
DI BLASIO [72], G. DORE - A. VENNI [76] and the subsequent papers
[90], [169], [170]. Many books about abstract evolution equations
and semigroups contain some chapters on analytic semigroups. See,
e. g. , E. HILLE - R. S. PHILLIPS [100]' S. G. KREIN [114], K.
YOSIDA [213], A. PAZY [166], H. TANABE [193], PH.
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