Linear and Quasilinear Parabolic Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Linear and Quasilinear Parabolic Problems write by Herbert Amann. This book was released on 2012-12-06. Linear and Quasilinear Parabolic Problems available in PDF, EPUB and Kindle. In this treatise we present the semigroup approach to quasilinear evolution equa of parabolic type that has been developed over the last ten years, approxi tions mately. It emphasizes the dynamic viewpoint and is sufficiently general and flexible to encompass a great variety of concrete systems of partial differential equations occurring in science, some of those being of rather 'nonstandard' type. In partic ular, to date it is the only general method that applies to noncoercive systems. Although we are interested in nonlinear problems, our method is based on the theory of linear holomorphic semigroups. This distinguishes it from the theory of nonlinear contraction semigroups whose basis is a nonlinear version of the Hille Yosida theorem: the Crandall-Liggett theorem. The latter theory is well-known and well-documented in the literature. Even though it is a powerful technique having found many applications, it is limited in its scope by the fact that, in concrete applications, it is closely tied to the maximum principle. Thus the theory of nonlinear contraction semigroups does not apply to systems, in general, since they do not allow for a maximum principle. For these reasons we do not include that theory.
Linear and Quasi-linear Equations of Parabolic Type
Linear and Quasi-linear Equations of Parabolic Type - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Linear and Quasi-linear Equations of Parabolic Type write by Olʹga A. Ladyženskaja. This book was released on 1988. Linear and Quasi-linear Equations of Parabolic Type available in PDF, EPUB and Kindle. Equations of parabolic type are encountered in many areas of mathematics and mathematical physics, and those encountered most frequently are linear and quasi-linear parabolic equations of the second order. In this volume, boundary value problems for such equations are studied from two points of view: solvability, unique or otherwise, and the effect of smoothness properties of the functions entering the initial and boundary conditions on the smoothness of the solutions.
Linear and Quasilinear Parabolic Problems
Linear and Quasilinear Parabolic Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Linear and Quasilinear Parabolic Problems write by Herbert Amann. This book was released on 1995-03-27. Linear and Quasilinear Parabolic Problems available in PDF, EPUB and Kindle. 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 last 10 years. This approach is based on the theory of linear nonautonomous parabolic evolution equations and on interpolation-extrapolation techniques. It is the only general method that applies to noncoercive quasilinear parabolic systems under nonlinear boundary conditions. The present first volume is devoted to a detailed study of nonautonomous linear parabolic evolution equations in general Banach spaces. It contains a careful exposition of the constant domain case, leading to some improvements of the classical Sobolevskii-Tanabe results. It also includes recent results for equations possessing constant interpolation spaces. In addition, systematic presentations of the theory of maximal regularity in spaces of continuous and Hölder continuous functions, and in Lebesgue spaces, are given. 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 many new results.
Linear and Quasilinear Parabolic Problems
Linear and Quasilinear Parabolic Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Linear and Quasilinear Parabolic Problems write by Herbert Amann. This book was released on 2019-04-16. Linear and Quasilinear Parabolic Problems available in PDF, EPUB and Kindle. This volume discusses an in-depth theory of function spaces in an Euclidean setting, including several new features, not previously covered in the literature. In particular, it develops a unified theory of anisotropic Besov and Bessel potential spaces on Euclidean corners, with infinite-dimensional Banach spaces as targets. It especially highlights the most important subclasses of Besov spaces, namely Slobodeckii and Hölder spaces. In this case, no restrictions are imposed on the target spaces, except for reflexivity assumptions in duality results. In this general setting, the author proves sharp embedding, interpolation, and trace theorems, point-wise multiplier results, as well as Gagliardo-Nirenberg estimates and generalizations of Aubin-Lions compactness theorems. The results presented pave the way for new applications in situations where infinite-dimensional target spaces are relevant – in the realm of stochastic differential equations, for example.
Linear and Quasilinear Parabolic Systems: Sobolev Space Theory
Linear and Quasilinear Parabolic Systems: Sobolev Space Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Linear and Quasilinear Parabolic Systems: Sobolev Space Theory write by David Hoff. This book was released on 2020-11-18. Linear and Quasilinear Parabolic Systems: Sobolev Space Theory available in PDF, EPUB and Kindle. This monograph presents a systematic theory of weak solutions in Hilbert-Sobolev spaces of initial-boundary value problems for parabolic systems of partial differential equations with general essential and natural boundary conditions and minimal hypotheses on coefficients. Applications to quasilinear systems are given, including local existence for large data, global existence near an attractor, the Leray and Hopf theorems for the Navier-Stokes equations and results concerning invariant regions. Supplementary material is provided, including a self-contained treatment of the calculus of Sobolev functions on the boundaries of Lipschitz domains and a thorough discussion of measurability considerations for elements of Bochner-Sobolev spaces. This book will be particularly useful both for researchers requiring accessible and broadly applicable formulations of standard results as well as for students preparing for research in applied analysis. Readers should be familiar with the basic facts of measure theory and functional analysis, including weak derivatives and Sobolev spaces. Prior work in partial differential equations is helpful but not required.
