Linear and Quasilinear Parabolic Problems
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Home > Mathematics and Science Textbooks > Mathematics > Calculus and mathematical analysis > Differential calculus and equations > Linear and Quasilinear Parabolic Problems: Volume I: Abstract Linear Theory(89 Monographs in Mathematics)
Linear and Quasilinear Parabolic Problems: Volume I: Abstract Linear Theory(89 Monographs in Mathematics)

Linear and Quasilinear Parabolic Problems: Volume I: Abstract Linear Theory(89 Monographs in Mathematics)


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About the Book

This treatise gives an exposition of the functional analytical approach to quasilinear parabolic evolution equations, developed to a large extent by the author during the 1980s. This approach is based on the theory of nonlinear non-autonomous parabolic evolution equations and on interpolation-extrapolation techniques. It is the only general method that applies to non-coercive quasilinear parabolic systems under nonlinear boundary conditions. This first volume is devoted to a detailed study of non-autonomous linear parabolic evolution equations in general Banach spaces. It contains an exposition of the constant domain case, leading to some improvements of the classical Sobolevski-Tanabe results. It also includes recent results for equations possessing constant interpolation spaces. In addition, the book provides systematic presentations of the theory of maximal regularity in spaces of continuous and Hoelder continuous functions, and in Lebesgue spaces. It includes related recent theorems in the field of harmonic analysis in Banach spaces and on operators possessing bounded imaginary powers. Lastly, there is a complete presentation of the technique of interpolation-extrapolation spaces and of evolution equations in those spaces, containing new results.

Table of Contents:
Notations and Conventions.- 1 Topological Spaces.- 2 Locally Convex Spaces.- 3 Complexifications.- 4 Unbounded Linear Operators.- 5 General Conventions.- I Generators and Interpolation.- 1 Generators of Analytic Semigroups.- 2 Interpolation Functors.- II Cauchy Problems and Evolution Operators.- 1 Linear Cauchy Problems.- 2 Parabolic Evolution Operators.- 3 Linear Volterra Integral Equations.- 4 Existence of Evolution Operators.- 5 Stability Estimates.- 6 Invariance and Positivity.- III Maximal Regularity.- 1 General Principles.- 2 Maximal Hölder Regularity.- 3 Maximal Continuous Regularity.- 4 Maximal Sobolev Regularity.- IV Variable Domains.- 1 Higher Regularity.- 2 Constant Interpolation Spaces.- 3 Maximal Regularity.- V Scales of Banach Spaces.- 1 Banach Scales.- 2 Evolution Equations in Banach Scales.- List of Symbols.


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Product Details
  • ISBN-13: 9783764351144
  • Publisher: Birkhauser Verlag AG
  • Publisher Imprint: Birkhauser Verlag AG
  • Height: 235 mm
  • No of Pages: 338
  • Returnable: Y
  • Sub Title: Volume I: Abstract Linear Theory
  • ISBN-10: 3764351144
  • Publisher Date: 27 Mar 1995
  • Binding: Hardback
  • Language: English
  • Returnable: Y
  • Series Title: 89 Monographs in Mathematics
  • Width: 155 mm


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Linear and Quasilinear Parabolic Problems: Volume I: Abstract Linear Theory(89 Monographs in Mathematics)
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