Critical Parabolic Type Problems

Author : Tomasz W. Dłotko,Yejuan Wang
Publisher : Walter de Gruyter GmbH & Co KG
Page : 300 pages
File Size : 43,5 Mb
Release : 2020-05-05
Category : Mathematics
ISBN : 9783110599831

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Critical Parabolic-Type Problems by Tomasz W. Dłotko,Yejuan Wang Pdf

This self-contained book covers the theory of semilinear equations with sectorial operator going back to the studies of Yosida, Henry, and Pazy, which are deeply extended nowadays. The treatment emphasizes existence-uniqueness theory as a topic of functional analysis and examines abstract evolutionary equations, with applications to the Navier-Stokes system, the quasi-geostrophic equation, and fractional reaction-diffusion equations.

Author : Prof. Dr. Pavol Quittner,Prof. Dr. Philippe Souplet
Publisher : Springer
Page : 719 pages
File Size : 55,6 Mb
Release : 2019-06-13
Category : Mathematics
ISBN : 9783030182229

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Superlinear Parabolic Problems by Prof. Dr. Pavol Quittner,Prof. Dr. Philippe Souplet Pdf

This book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems. This class of problems contains, in particular, a number of reaction-diffusion systems which arise in various mathematical models, especially in chemistry, physics and biology. The first two chapters introduce to the field and enable the reader to get acquainted with the main ideas by studying simple model problems, respectively of elliptic and parabolic type. The subsequent three chapters are devoted to problems with more complex structure; namely, elliptic and parabolic systems, equations with gradient depending nonlinearities, and nonlocal equations. They include many developments which reflect several aspects of current research. Although the techniques introduced in the first two chapters provide efficient tools to attack some aspects of these problems, they often display new phenomena and specifically different behaviors, whose study requires new ideas. Many open problems are mentioned and commented. The book is self-contained and up-to-date, it has a high didactic quality. It is devoted to problems that are intensively studied but have not been treated so far in depth in the book literature. The intended audience includes graduate and postgraduate students and researchers working in the field of partial differential equations and applied mathematics. The first edition of this book has become one of the standard references in the field. This second edition provides a revised text and contains a number of updates reflecting significant recent advances that have appeared in this growing field since the first edition.

Author : Tomasz W. Dłotko,Yejuan Wang
Publisher : Walter de Gruyter GmbH & Co KG
Page : 217 pages
File Size : 45,8 Mb
Release : 2020-05-05
Category : Mathematics
ISBN : 9783110598681

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Critical Parabolic-Type Problems by Tomasz W. Dłotko,Yejuan Wang Pdf

This self-contained book covers the theory of semilinear equations with sectorial operator going back to the studies of Yosida, Henry, and Pazy, which are deeply extended nowadays. The treatment emphasizes existence-uniqueness theory as a topic of functional analysis and examines abstract evolutionary equations, with applications to the Navier-Stokes system, the quasi-geostrophic equation, and fractional reaction-diffusion equations.

Author : Pavol Quittner,Philippe Souplet
Publisher : Springer Science & Business Media
Page : 593 pages
File Size : 51,8 Mb
Release : 2007-12-16
Category : Mathematics
ISBN : 9783764384425

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Superlinear Parabolic Problems by Pavol Quittner,Philippe Souplet Pdf

This book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems. This class of problems contains, in particular, a number of reaction-diffusion systems which arise in various mathematical models, especially in chemistry, physics and biology. The book is self-contained and up-to-date, taking special care on the didactical preparation of the material. It is devoted to problems that are intensively studied but have not been treated thus far in depth in the book literature.

Author : Avner Friedman
Publisher : Unknown
Page : 376 pages
File Size : 41,8 Mb
Release : 1964
Category : Differential equations, Parabolic
ISBN : UOM:39076006346840

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Partial Differential Equations of Parabolic Type by Avner Friedman Pdf

Author : Alessandra Lunardi
Publisher : Springer Science & Business Media
Page : 452 pages
File Size : 49,6 Mb
Release : 1995-01-27
Category : Mathematics
ISBN : 3764351721

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Analytic Semigroups and Optimal Regularity in Parabolic Problems by Alessandra Lunardi Pdf

The book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be fruitfully applied to the study of parabolic problems. Particular attention is paid to optimal regularity results in linear equations. Furthermore, these results are used to study several other problems, especially fully nonlinear ones. Owing to the new unified approach chosen, known theorems are presented from a novel perspective and new results are derived. The book is self-contained. It is addressed to PhD students and researchers interested in abstract evolution equations and in parabolic partial differential equations and systems. It gives a comprehensive overview on the present state of the art in the field, teaching at the same time how to exploit its basic techniques. - - - This very interesting book provides a systematic treatment of the basic theory of analytic semigroups and abstract parabolic equations in general Banach spaces, and how this theory may be used in the study of parabolic partial differential equations; it takes into account the developments of the theory during the last fifteen years. (...) For instance, optimal regularity results are a typical feature of abstract parabolic equations; they are comprehensively studied in this book, and yield new and old regularity results for parabolic partial differential equations and systems. (Mathematical Reviews) Motivated by applications to fully nonlinear problems the approach is focused on classical solutions with continuous or Hölder continuous derivatives. (Zentralblatt MATH)

Author : V. Thomee
Publisher : Springer
Page : 243 pages
File Size : 40,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540387930

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Galerkin Finite Element Methods for Parabolic Problems by V. Thomee Pdf

Author : Gary M. Lieberman
Publisher : World Scientific
Page : 472 pages
File Size : 45,8 Mb
Release : 1996
Category : Mathematics
ISBN : 981022883X

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Second Order Parabolic Differential Equations by Gary M. Lieberman Pdf

Introduction. Maximum principles. Introduction to the theory of weak solutions. Hölder estimates. Existence, uniqueness, and regularity of solutions. Further theory of weak solutions. Strong solutions. Fixed point theorems and their applications. Comparison and maximum principles. Boundary gradient estimates. Global and local gradient bounds. Hölder gradient estimates and existence theorems. The oblique derivative problem for quasilinear parabolic equations. Fully nonlinear equations. Introduction. Monge-Ampère and Hessian equations.

Author : M.J. Valtonen
Publisher : Springer Science & Business Media
Page : 418 pages
File Size : 52,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400929173

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The Few Body Problem by M.J. Valtonen Pdf

th Coinciding with the 300 anniversary of the publication of Newton's Principia The International Astronomical Union organized the colloquium No. 96 "The Few Body Problem" in Turku, Finland, June 14.-19.1987. It provided an opportunity to review the progress in the very field which caused Newton a headache, as Victor Szebehely reminded the audience in his introductory remarks. It is a measure of the difficulty and complication of the few body problem that even after 300 years so many aspects of the problem are still unsolved. To quote Szebehely again, "Sir Isaac established the rules, Poincare presented the challenges". Many of these challenges are reviewed in the present proceedings. The gravitational few body problem cuts across the borders of established disciplines. The participants of the colloquium came from departments as different as Aerospace Engineering, Astronomy, Theoretical Physics, Physics, Mathematics, Applied Mathematics, Computer Science, Planetology, Geodesy, Celestial Mechanics and Space Science. The few body problem is a problem of practical significance in many fields and the main aim of the colloquium was to bring together people with research interests in this area, many of whom normally attend different conferences.

Author : A Alvino,P Buonocore,V Ferone,E Giarrusso,G Trombetti,S Matarasso
Publisher : CRC Press
Page : 236 pages
File Size : 40,5 Mb
Release : 1996-05-15
Category : Mathematics
ISBN : 0582259703

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Progress in Elliptic and Parabolic Partial Differential Equations by A Alvino,P Buonocore,V Ferone,E Giarrusso,G Trombetti,S Matarasso Pdf

This Research Note collects reports of the invited plenary addresses given during the conference Elliptic and Parabolic Partial Differential Equations and Applications held in Capri, Italy, 19-23 September 1994. The conference was devoted to new developments in partial differential equations of elliptic and parabolic type and to their applications in various fields.

Author : Dung Le
Publisher : Walter de Gruyter GmbH & Co KG
Page : 236 pages
File Size : 46,5 Mb
Release : 2022-10-24
Category : Mathematics
ISBN : 9783110795134

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Cross Diffusion Systems by Dung Le Pdf

The introduction of cross diffusivity opens many questions in the theory of reactiondiffusion systems. This book will be the first to investigate such problems presenting new findings for researchers interested in studying parabolic and elliptic systems where classical methods are not applicable. In addition, The Gagliardo-Nirenberg inequality involving BMO norms is improved and new techniques are covered that will be of interest. This book also provides many open problems suitable for interested Ph.D students.

Author : Jesús Garcia-Falset,Khalid Latrach
Publisher : Walter de Gruyter GmbH & Co KG
Page : 466 pages
File Size : 46,5 Mb
Release : 2023-03-06
Category : Mathematics
ISBN : 9783111031811

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Nonlinear Functional Analysis and Applications by Jesús Garcia-Falset,Khalid Latrach Pdf

Nonlinear functional analysis is a central subject of mathematics with applications in many areas of geometry, analysis, fl uid and elastic mechanics, physics, chemistry, biology, control theory, optimization, game theory, economics etc. This work is devoted, in a self-contained way, to several subjects of this topic such as theory of accretive operators in Banach spaces, theory of abstract Cauchy problem, metric and topological fixed point theory. Special emphasis is given to the study how these theories can be used to obtain existence and uniqueness of solutions for several types of evolution and stationary equations. In particular, equations arising in dynamical population and neutron transport equations are discussed.

Author : Jesús Ildefonso Díaz,David Gómez-Castro,Tatiana A. Shaposhnikova
Publisher : Walter de Gruyter GmbH & Co KG
Page : 200 pages
File Size : 47,7 Mb
Release : 2021-06-21
Category : Mathematics
ISBN : 9783110648997

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Nonlinear Reaction-Diffusion Processes for Nanocomposites by Jesús Ildefonso Díaz,David Gómez-Castro,Tatiana A. Shaposhnikova Pdf

The behavior of materials at the nanoscale is a key aspect of modern nanoscience and nanotechnology. This book presents rigorous mathematical techniques showing that some very useful phenomenological properties which can be observed at the nanoscale in many nonlinear reaction-diffusion processes can be simulated and justified mathematically by means of homogenization processes when a certain critical scale is used in the corresponding framework.

Author : Catherine Bandle,Alfred Wagner
Publisher : Walter de Gruyter GmbH & Co KG
Page : 292 pages
File Size : 40,7 Mb
Release : 2023-06-19
Category : Mathematics
ISBN : 9783111025438

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Shape Optimization by Catherine Bandle,Alfred Wagner Pdf

This book investigates how domain dependent quantities from geometry and physics behave when the domain is perturbed. Of particular interest are volume- and perimeter-preserving perturbations. The first and second derivatives with respect to the perturbation are exploited for domain functionals like eigenvalues, energies and geometrical quantities. They provide necessary conditions for optimal domains and are useful when global approaches like symmetrizations fail. The book is exampledriven and illustrates the usefulness of domain variations in various applications.

Author : Nikolai Kutev,Tsviatko Rangelov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 158 pages
File Size : 54,5 Mb
Release : 2022-10-24
Category : Mathematics
ISBN : 9783110980370

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Hardy Inequalities and Applications by Nikolai Kutev,Tsviatko Rangelov Pdf

This book derives new Hardy inequalities with double singular weights - at an interior point and on the boundary of the domain. We focus on the optimality of Hardy constant and on its attainability. Applications include: results about existence\nonexistence and controllability for parabolic equations with double singular potentials; estimates from below of the fi rst eigenvalue of p-Laplacian with Dirichlet boundary conditions.