Nonlocal and Abstract Parabolic Equations and Their Applications
Author: Piotr Mucha
Publisher:
Published: 2009
Total Pages: 332
ISBN-13:
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General Parabolic Mixed Order Systems in Lp and Applications
Author: Robert Denk
Publisher: Springer Science & Business Media
Published: 2013-11-22
Total Pages: 254
ISBN-13: 3319020005
DOWNLOAD EBOOKIn this text, a theory for general linear parabolic partial differential equations is established which covers equations with inhomogeneous symbol structure as well as mixed-order systems. Typical applications include several variants of the Stokes system and free boundary value problems. We show well-posedness in Lp-Lq-Sobolev spaces in time and space for the linear problems (i.e., maximal regularity) which is the key step for the treatment of nonlinear problems. The theory is based on the concept of the Newton polygon and can cover equations which are not accessible by standard methods as, e.g., semigroup theory. Results are obtained in different types of non-integer Lp-Sobolev spaces as Besov spaces, Bessel potential spaces, and Triebel–Lizorkin spaces. The last-mentioned class appears in a natural way as traces of Lp-Lq-Sobolev spaces. We also present a selection of applications in the whole space and on half-spaces. Among others, we prove well-posedness of the linearizations of the generalized thermoelastic plate equation, the two-phase Navier–Stokes equations with Boussinesq–Scriven surface, and the Lp-Lq two-phase Stefan problem with Gibbs–Thomson correction.
Nonlinear Evolution Equations And Their Applications - Proceedings Of The Luso-chinese Symposium
Author: Tatsien Li
Publisher: World Scientific
Published: 1999-08-31
Total Pages: 334
ISBN-13: 9814543446
DOWNLOAD EBOOKThis book discusses recent trends and developments in the area of nonlinear evolution equations. It is a collection of invited lectures on the following topics: nonlinear parabolic equations (systems); nonlinear hyperbolic systems; free boundary problems; conservation laws and shock waves; travelling and solitary waves; regularity, stability and singularity, etc.
Fractional-in-Time Semilinear Parabolic Equations and Applications
Author: Ciprian G. Gal
Publisher: Springer Nature
Published: 2020-09-23
Total Pages: 193
ISBN-13: 3030450430
DOWNLOAD EBOOKThis book provides a unified analysis and scheme for the existence and uniqueness of strong and mild solutions to certain fractional kinetic equations. This class of equations is characterized by the presence of a nonlinear time-dependent source, generally of arbitrary growth in the unknown function, a time derivative in the sense of Caputo and the presence of a large class of diffusion operators. The global regularity problem is then treated separately and the analysis is extended to some systems of fractional kinetic equations, including prey-predator models of Volterra–Lotka type and chemical reactions models, all of them possibly containing some fractional kinetics. Besides classical examples involving the Laplace operator, subject to standard (namely, Dirichlet, Neumann, Robin, dynamic/Wentzell and Steklov) boundary conditions, the framework also includes non-standard diffusion operators of "fractional" type, subject to appropriate boundary conditions. This book is aimed at graduate students and researchers in mathematics, physics, mathematical engineering and mathematical biology, whose research involves partial differential equations.
Collected Papers in Honor of Yoshihiro Shibata
Author: Tohru Ozawa
Publisher: Springer Nature
Published: 2023-01-01
Total Pages: 396
ISBN-13: 3031192524
DOWNLOAD EBOOKYoshihiro Shibata has made many significant contributions to the area of mathematical fluid mechanics over the course of his illustrious career, including landmark work on the Navier-Stokes equations. The papers collected here — on the occasion of his 70th birthday — are written by world-renowned researchers and celebrate his decades of outstanding achievements.
Topics in Applied Analysis and Optimisation
Author: Michael Hintermüller
Publisher: Springer Nature
Published: 2019-11-27
Total Pages: 406
ISBN-13: 3030331164
DOWNLOAD EBOOKThis volume comprises selected, revised papers from the Joint CIM-WIAS Workshop, TAAO 2017, held in Lisbon, Portugal, in December 2017. The workshop brought together experts from research groups at the Weierstrass Institute in Berlin and mathematics centres in Portugal to present and discuss current scientific topics and to promote existing and future collaborations. The papers include the following topics: PDEs with applications to material sciences, thermodynamics and laser dynamics, scientific computing, nonlinear optimization and stochastic analysis.
New Developments in the Analysis of Nonlocal Operators
Author: Donatella Danielli
Publisher: American Mathematical Soc.
Published: 2019-02-21
Total Pages: 226
ISBN-13: 1470441101
DOWNLOAD EBOOKThis volume contains the proceedings of the AMS Special Session on New Developments in the Analysis of Nonlocal Operators, held from October 28–30, 2016, at the University of St. Thomas, Minneapolis, Minnesota. Over the last decade there has been a resurgence of interest in problems involving nonlocal operators, motivated by applications in many areas such as analysis, geometry, and stochastic processes. Problems represented in this volume include uniqueness for weak solutions to abstract parabolic equations with fractional time derivatives, the behavior of the one-phase Bernoulli-type free boundary near a fixed boundary and its relation to a Signorini-type problem, connections between fractional powers of the spherical Laplacian and zeta functions from the analytic number theory and differential geometry, and obstacle problems for a class of not stable-like nonlocal operators for asset price models widely used in mathematical finance. The volume also features a comprehensive introduction to various aspects of the fractional Laplacian, with many historical remarks and an extensive list of references, suitable for beginners and more seasoned researchers alike.
Modern Analysis and Applications
Author: Vadim Adamyan
Publisher: Springer Science & Business Media
Published: 2009-08-29
Total Pages: 518
ISBN-13: 376439921X
DOWNLOAD EBOOKThis is the second of two volumes containing peer-reviewed research and survey papers based on talks at the International Conference on Modern Analysis and Applications. The papers describe the contemporary development of subjects influenced by Mark Krein.
Proceedings of the Conference on Differential & Difference Equations and Applications
Author: Ravi P. Agarwal
Publisher: Hindawi Publishing Corporation
Published: 2006
Total Pages: 1266
ISBN-13: 9789775945389
DOWNLOAD EBOOKNonlocal Diffusion Problems
Author: Fuensanta Andreu-Vaillo
Publisher: American Mathematical Soc.
Published: 2010
Total Pages: 274
ISBN-13: 0821852302
DOWNLOAD EBOOKNonlocal diffusion problems arise in a wide variety of applications, including biology, image processing, particle systems, coagulation models, and mathematical finance. These types of problems are also of great interest for their purely mathematical content. This book presents recent results on nonlocal evolution equations with different boundary conditions, starting with the linear theory and moving to nonlinear cases, including two nonlocal models for the evolution of sandpiles. Both existence and uniqueness of solutions are considered, as well as their asymptotic behaviour. Moreover, the authors present results concerning limits of solutions of the nonlocal equations as a rescaling parameter tends to zero. With these limit procedures the most frequently used diffusion models are recovered: the heat equation, the $p$-Laplacian evolution equation, the porous media equation, the total variation flow, a convection-diffusion equation and the local models for the evolution of sandpiles due to Aronsson-Evans-Wu and Prigozhin. Readers are assumed to be familiar with the basic concepts and techniques of functional analysis and partial differential equations. The text is otherwise self-contained, with the exposition emphasizing an intuitive understanding and results given with full proofs. It is suitable for graduate students or researchers. The authors cover a subject that has received a great deal of attention in recent years. The book is intended as a reference tool for a general audience in analysis and PDEs, including mathematicians, engineers, physicists, biologists, and others interested in nonlocal diffusion problems.
