Differential Equations on Measures and Functional Spaces - 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 Differential Equations on Measures and Functional Spaces write by Vassili Kolokoltsov. This book was released on 2019-06-20. Differential Equations on Measures and Functional Spaces available in PDF, EPUB and Kindle. This advanced book focuses on ordinary differential equations (ODEs) in Banach and more general locally convex spaces, most notably the ODEs on measures and various function spaces. It briefly discusses the fundamentals before moving on to the cutting edge research in linear and nonlinear partial and pseudo-differential equations, general kinetic equations and fractional evolutions. The level of generality chosen is suitable for the study of the most important nonlinear equations of mathematical physics, such as Boltzmann, Smoluchovskii, Vlasov, Landau-Fokker-Planck, Cahn-Hilliard, Hamilton-Jacobi-Bellman, nonlinear Schroedinger, McKean-Vlasov diffusions and their nonlocal extensions, mass-action-law kinetics from chemistry. It also covers nonlinear evolutions arising in evolutionary biology and mean-field games, optimization theory, epidemics and system biology, in general models of interacting particles or agents describing splitting and merging, collisions and breakage, mutations and the preferential-attachment growth on networks. The book is intended mainly for upper undergraduate and graduate students, but is also of use to researchers in differential equations and their applications. It particularly highlights the interconnections between various topics revealing where and how a particular result is used in other chapters or may be used in other contexts, and also clarifies the links between the languages of pseudo-differential operators, generalized functions, operator theory, abstract linear spaces, fractional calculus and path integrals.
Functional Spaces for the Theory of Elliptic Partial Differential Equations
Functional Spaces for the Theory of Elliptic Partial Differential 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 Functional Spaces for the Theory of Elliptic Partial Differential Equations write by Françoise Demengel. This book was released on 2012-01-24. Functional Spaces for the Theory of Elliptic Partial Differential Equations available in PDF, EPUB and Kindle. The theory of elliptic boundary problems is fundamental in analysis and the role of spaces of weakly differentiable functions (also called Sobolev spaces) is essential in this theory as a tool for analysing the regularity of the solutions. This book offers on the one hand a complete theory of Sobolev spaces, which are of fundamental importance for elliptic linear and non-linear differential equations, and explains on the other hand how the abstract methods of convex analysis can be combined with this theory to produce existence results for the solutions of non-linear elliptic boundary problems. The book also considers other kinds of functional spaces which are useful for treating variational problems such as the minimal surface problem. The main purpose of the book is to provide a tool for graduate and postgraduate students interested in partial differential equations, as well as a useful reference for researchers active in the field. Prerequisites include a knowledge of classical analysis, differential calculus, Banach and Hilbert spaces, integration and the related standard functional spaces, as well as the Fourier transformation on the Schwartz space. There are complete and detailed proofs of almost all the results announced and, in some cases, more than one proof is provided in order to highlight different features of the result. Each chapter concludes with a range of exercises of varying levels of difficulty, with hints to solutions provided for many of them.
Functional Analysis, Sobolev Spaces and Partial Differential Equations
Functional Analysis, Sobolev Spaces and Partial Differential 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 Functional Analysis, Sobolev Spaces and Partial Differential Equations write by Haim Brezis. This book was released on 2010-11-02. Functional Analysis, Sobolev Spaces and Partial Differential Equations available in PDF, EPUB and Kindle. This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.
Applied Stochastic Differential Equations
Applied Stochastic Differential 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 Applied Stochastic Differential Equations write by Simo Särkkä. This book was released on 2019-05-02. Applied Stochastic Differential Equations available in PDF, EPUB and Kindle. With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Integration in Hilbert Space
Integration in Hilbert Space - 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 Integration in Hilbert Space write by A. V. Skorohod. This book was released on 2012-12-06. Integration in Hilbert Space available in PDF, EPUB and Kindle. Integration in function spaces arose in probability theory when a gen eral theory of random processes was constructed. Here credit is cer tainly due to N. Wiener, who constructed a measure in function space, integrals-with respect to which express the mean value of functionals of Brownian motion trajectories. Brownian trajectories had previously been considered as merely physical (rather than mathematical) phe nomena. A. N. Kolmogorov generalized Wiener's construction to allow one to establish the existence of a measure corresponding to an arbitrary random process. These investigations were the beginning of the development of the theory of stochastic processes. A considerable part of this theory involves the solution of problems in the theory of measures on function spaces in the specific language of stochastic pro cesses. For example, finding the properties of sample functions is connected with the problem of the existence of a measure on some space; certain problems in statistics reduce to the calculation of the density of one measure w. r. t. another one, and the study of transformations of random processes leads to the study of transformations of function spaces with measure. One must note that the language of probability theory tends to obscure the results obtained in these areas for mathematicians working in other fields. Another dir,ection leading to the study of integrals in function space is the theory and application of differential equations. A. N.
