Isolated Singularities in Partial Differential Inequalities - 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 Isolated Singularities in Partial Differential Inequalities write by Marius Ghergu. This book was released on 2016-01-25. Isolated Singularities in Partial Differential Inequalities available in PDF, EPUB and Kindle. In this monograph, the authors present some powerful methods for dealing with singularities in elliptic and parabolic partial differential inequalities. Here, the authors take the unique approach of investigating differential inequalities rather than equations, the reason being that the simplest way to study an equation is often to study a corresponding inequality; for example, using sub and superharmonic functions to study harmonic functions. Another unusual feature of the present book is that it is based on integral representation formulae and nonlinear potentials, which have not been widely investigated so far. This approach can also be used to tackle higher order differential equations. The book will appeal to graduate students interested in analysis, researchers in pure and applied mathematics, and engineers who work with partial differential equations. Readers will require only a basic knowledge of functional analysis, measure theory and Sobolev spaces.
Partial Differential Inequalities with Nonlinear Convolution Terms
Partial Differential Inequalities with Nonlinear Convolution Terms - 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 Partial Differential Inequalities with Nonlinear Convolution Terms write by Marius Ghergu. This book was released on 2023-01-01. Partial Differential Inequalities with Nonlinear Convolution Terms available in PDF, EPUB and Kindle. This brief research monograph uses modern mathematical methods to investigate partial differential equations with nonlinear convolution terms, enabling readers to understand the concept of a solution and its asymptotic behavior. In their full generality, these inequalities display a non-local structure. Classical methods, such as maximum principle or sub- and super-solution methods, do not apply to this context. This work discusses partial differential inequalities (instead of differential equations) for which there is no variational setting. This current work brings forward other methods that prove to be useful in understanding the concept of a solution and its asymptotic behavior related to partial differential inequalities with nonlinear convolution terms. It promotes and illustrates the use of a priori estimates, Harnack inequalities, and integral representation of solutions. One of the first monographs on this rapidly expanding field, the present work appeals to graduate and postgraduate students as well as to researchers in the field of partial differential equations and nonlinear analysis.
Singularities of Solutions of Second-Order Quasilinear Equations
Singularities of Solutions of Second-Order Quasilinear Equations - 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 Singularities of Solutions of Second-Order Quasilinear Equations write by Laurent Veron. This book was released on 1996-08-01. Singularities of Solutions of Second-Order Quasilinear Equations available in PDF, EPUB and Kindle. This text examines the singularity problem for solutions of elliptic and parabolic quasilinear equations of second order.
Singular Solutions of Nonlinear Elliptic and Parabolic Equations
Singular Solutions of Nonlinear Elliptic and Parabolic Equations - 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 Singular Solutions of Nonlinear Elliptic and Parabolic Equations write by Alexander A. Kovalevsky. This book was released on 2016-03-21. Singular Solutions of Nonlinear Elliptic and Parabolic Equations available in PDF, EPUB and Kindle. This monograph looks at several trends in the investigation of singular solutions of nonlinear elliptic and parabolic equations. It discusses results on the existence and properties of weak and entropy solutions for elliptic second-order equations and some classes of fourth-order equations with L1-data and questions on the removability of singularities of solutions to elliptic and parabolic second-order equations in divergence form. It looks at localized and nonlocalized singularly peaking boundary regimes for different classes of quasilinear parabolic second- and high-order equations in divergence form. The book will be useful for researchers and post-graduate students that specialize in the field of the theory of partial differential equations and nonlinear analysis. Contents: Foreword Part I: Nonlinear elliptic equations with L^1-data Nonlinear elliptic equations of the second order with L^1-data Nonlinear equations of the fourth order with strengthened coercivity and L^1-data Part II: Removability of singularities of the solutions of quasilinear elliptic and parabolic equations of the second order Removability of singularities of the solutions of quasilinear elliptic equations Removability of singularities of the solutions of quasilinear parabolic equations Quasilinear elliptic equations with coefficients from the Kato class Part III: Boundary regimes with peaking for quasilinear parabolic equations Energy methods for the investigation of localized regimes with peaking for parabolic second-order equations Method of functional inequalities in peaking regimes for parabolic equations of higher orders Nonlocalized regimes with singular peaking Appendix: Formulations and proofs of the auxiliary results Bibliography
Superlinear Parabolic Problems
Superlinear 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 Superlinear Parabolic Problems write by Prof. Dr. Pavol Quittner. This book was released on 2019-06-13. Superlinear Parabolic Problems available in PDF, EPUB and Kindle. 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.
