Analytic Semigroups and Optimal Regularity in Parabolic Problems

Első borító
Springer Science & Business Media, 1995. jan. 1. - 424 oldal
1 Ismertető
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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Tartalomjegyzék

spaces of continuous
6
Interpolation theory
11
Analytic semigroups and intermediate spaces
33
Generation of analytic semigroups by elliptic operators
69
Nonhomogeneous equations
121
This
153
Linear parabolic problems
173
Linear nonautonomous equations
211
Semilinear equations
253
Fully nonlinear equations
287
Asymptotic behavior in fully nonlinear equations
337
Spectrum and resolvent
399
Bibliography
411
Index
423
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A szerzőről (1995)

Alessandra Lunardi is a professor of mathematics at the University of Parma, Italy.

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