Download or read book Continuous Dependence on Modeling in the Cauchy Problem for Second order Nonlinear Partial Differential Equations written by Allan David Bennett and published by . This book was released on 1986 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Singular and Degenerate Cauchy Problems written by and published by Academic Press. This book was released on 1977-01-13 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering
Download or read book Partial Differential Equations written by Marcelo Epstein and published by Springer. This book was released on 2017-04-29 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in continuum physics. Four chapters are devoted to a detailed treatment of the single first-order PDE, including shock waves and genuinely non-linear models, with applications to traffic design and gas dynamics. The rest of the book deals with second-order equations. In the treatment of hyperbolic equations, geometric arguments are used whenever possible and the analogy with discrete vibrating systems is emphasized. The diffusion and potential equations afford the opportunity of dealing with questions of uniqueness and continuous dependence on the data, the Fourier integral, generalized functions (distributions), Duhamel's principle, Green's functions and Dirichlet and Neumann problems. The target audience primarily comprises graduate students in engineering, but the book may also be beneficial for lecturers, and research experts both in academia in industry.
Download or read book Practical Course In Differential Equations And Mathematical Modelling A Classical And New Methods Nonlinear Mathematical Models Symmetry And Invariance Principles written by Nail H Ibragimov and published by World Scientific Publishing Company. This book was released on 2009-11-19 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments. The book — which aims to present new mathematical curricula based on symmetry and invariance principles — is tailored to develop analytic skills and “working knowledge” in both classical and Lie's methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundamental solution, etc. easy to follow and interesting for students. The book is based on the author's extensive teaching experience at Novosibirsk and Moscow universities in Russia, Collège de France, Georgia Tech and Stanford University in the United States, universities in South Africa, Cyprus, Turkey, and Blekinge Institute of Technology (BTH) in Sweden. The new curriculum prepares students for solving modern nonlinear problems and will essentially be more appealing to students compared to the traditional way of teaching mathematics.
Download or read book The Characteristic Method and Its Generalizations for First Order Nonlinear Partial Differential Equations written by Tran Duc Van and published by CRC Press. This book was released on 1999-06-25 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite decades of research and progress in the theory of generalized solutions to first-order nonlinear partial differential equations, a gap between the local and the global theories remains: The Cauchy characteristic method yields the local theory of classical solutions. Historically, the global theory has principally depended on the vanishing viscosity method. The authors of this volume help bridge the gap between the local and global theories by using the characteristic method as a basis for setting a theoretical framework for the study of global generalized solutions. That is, they extend the smooth solutions obtained by the characteristic method. The authors offer material previously unpublished in book form, including treatments of the life span of classical solutions, the construction of singularities of generalized solutions, new existence and uniqueness theorems on minimax solutions, differential inequalities of Haar type and their application to the uniqueness of global, semi-classical solutions, and Hopf-type explicit formulas for global solutions. These subjects yield interesting relations between purely mathematical theory and the applications of first-order nonlinear PDEs. The Characteristic Method and Its Generalizations for First-Order Nonlinear Partial Differential Equations represents a comprehensive exposition of the authors' works over the last decade. The book is self-contained and assumes only basic measure theory, topology, and ordinary differential equations as prerequisites. With its innovative approach, new results, and many applications, it will prove valuable to mathematicians, physicists, and engineers and especially interesting to researchers in nonlinear PDEs, differential inequalities, multivalued analysis, differential games, and related topics in applied analysis.
Download or read book Non Standard and Improperly Posed Problems written by William F. Ames and published by Elsevier. This book was released on 1997-07-07 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by two international experts in the field, this book is the first unified survey of the advances made in the last 15 years on key non-standard and improperly posed problems for partial differential equations.This reference for mathematicians, scientists, and engineers provides an overview of the methodology typically used to study improperly posed problems. It focuses on structural stability--the continuous dependence of solutions on the initial conditions and the modeling equations--and on problems for which data are only prescribed on part of the boundary. The book addresses continuous dependence on initial-time and spatial geometry and on modeling backward and forward in time. It covers non-standard or non-characteristic problems, such as the sideways problem for a heat or hyberbolic equation and the Cauchy problem for the Laplace equation and other elliptic equations. The text also presents other relevant improperly posed problems, including the uniqueness and continuous dependence for singular equations, the spatial decay in improperly posed parabolicproblems, the uniqueness for the backward in time Navier-Stokes equations on an unbounded domain, the improperly posed problems for dusty gases, the linear thermoelasticity, and the overcoming Holder continuity and image restoration. Provides the first unified survey of the advances made in the last 15 years in the field Includes an up-to-date compendium of the mathematical literature on these topics
Download or read book Lectures on Cauchy s Problem in Linear Partial Differential Equations written by Jacques Hadamard and published by . This book was released on 1923 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Equations in the Applied Sciences written by W. F. Ames and published by Academic Press. This book was released on 1991-08-16 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Equations in the Applied Sciences
Download or read book Partial Differential Equations in Action written by Sandro Salsa and published by Springer. This book was released on 2015-04-24 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems.
Download or read book Para Differential Calculus and Applications to the Cauchy Problem for Nonlinear Systems written by Guy Métivier and published by Edizioni della Normale. This book was released on 2008-07-17 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main aim is to present at the level of beginners several modern tools of micro-local analysis which are useful for the mathematical study of nonlinear partial differential equations. The core of these notes is devoted to a presentation of the para-differential techniques, which combine a linearization procedure for nonlinear equations, and a symbolic calculus which mimics or extends the classical calculus of Fourier multipliers. These methods apply to many problems in nonlinear PDE’s such as elliptic equations, propagation of singularities, boundary value problems, shocks or boundary layers. However, in these introductory notes, we have chosen to illustrate the theory on two selected and relatively simple examples, which allow becoming familiar with the techniques. They concern the well posed-ness of the Cauchy problem for systems of nonlinear PDE's, firstly hyperbolic systems and secondly coupled systems of Schrödinger equations which arise in various models of wave propagation.
Download or read book Existence and Number of Global Solutions to Model Nonlinear Partial Differential Equations written by and published by . This book was released on 2005 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation we studied nonlinear partial differential equations in two different directions. We apply the bifurcation theory to investigate a number of positive solutions of the semilinear Dirichlet boundary value problem on a n-dimensional ball for the second order elliptic equation with periodic nonlinearity containing a positive parameter. Our approach appeals to the well known results of B. Gidas, W.-M. Ni, L. Nirenberg, the bifurcation theorems of M.G. Crandall and P.H. Rabinowitz, and the stationary phase method. Further, we investigate the issue of global existence of the solutions of the Cauchy problem for the semilinear Tricomi-type equations, appearing in the boundary value problems problems of gas dynamics. We study Cauchy problem trough integral equation and give some sufficient conditions for the existence of the global weak solutions. We prove necessity of these conditions. We obtain necessary condition for the existence of the self-similar solutions for the semilinear Tricomi-type equation. In our approach we employ the fundamental solution and the Lp-Lq estimates for the linear Tricomi-type equations.
Download or read book Nonlinear Diffusion Equations written by Zhuoqun Wu and published by World Scientific. This book was released on 2001 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which enrich the theory of partial differential equations. This book provides a comprehensive presentation of the basic problems, main results and typical methods for nonlinear diffusion equations with degeneracy. Some results for equations with singularity are touched upon. Contents: Newtonian Filtration Equations: Existence and Uniqueness of Solutions: One Dimensional Case; Existence and Uniqueness of Solutions: Higher Dimensional Case; Regularity of Solutions: One Dimensional Case; Regularity of Solutions: Higher Dimensional Case; Properties of the Free Boundary: One Dimensional Case; Properties of the Free Boundary: Higher Dimensional Case; Initial Trace of Solutions; Other Problems; Non-Newtonian Filtration Equations: Existence of Solutions; Harnack Inequality and Initial Trace of Solutions; Regularity of Solutions; Uniqueness of Solutions; Properties of the Free Boundary; Other Problems; General Quasilinear Equations of Second Order: Weakly Degenerate Equations in One Dimension; Weakly Degenerate Equations in Higher Dimension; Strongly Degenerate Equations in One Dimension; Degenerate Equations in Higher Dimension without Terms of Lower Order; General Strongly Degenerate Equations in Higher Dimension; Classes BV and BV x; Nonlinear Diffusion Equations of Higher Order: Similarity Solutions of a Fourth Order Equation; Equations with Double-Degeneracy; CahnOCoHilliard Equation with Constant Mobility; CahnOCoHilliard Equations with Positive Concentration Dependent Mobility; Thin Film Equation; CahnOCoHilliard Equation with Degenerate Mobility. Readership: Researchers, lecturers and graduate students in the fields of analysis and differential equations, mathematical physics and fluid mechanics."
Download or read book Advances In Nonlinear Partial Differential Equations And Stochastics written by S Kawashima and published by World Scientific. This book was released on 1998-06-17 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past two decades, there has been great progress in the theory of nonlinear partial differential equations. This book describes the progress, focusing on interesting topics in gas dynamics, fluid dynamics, elastodynamics etc. It contains ten articles, each of which discusses a very recent result obtained by the author. Some of these articles review related results.
Download or read book Recent Developments in Nonlinear Partial Differential Equations written by Donatella Danielli and published by American Mathematical Soc.. This book was released on 2007 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains research and expository articles based on talks presented at the 2nd Symposium on Analysis and PDEs, held at Purdue University. The Symposium focused on topics related to the theory and applications of nonlinear partial differential equations that are at the forefront of current international research. Papers in this volume provide a comprehensive account of many of the recent developments in the field. The topics featured in this volume include: kinetic formulations of nonlinear PDEs; recent unique continuation results and their applications; concentrations and constrained Hamilton-Jacobi equations; nonlinear Schrodinger equations; quasiminimal sets for Hausdorff measures; Schrodinger flows into Kahler manifolds; and parabolic obstacle problems with applications to finance. The clear and concise presentation in many articles makes this volume suitable for both researchers and graduate students.
Download or read book Error Estimates for Well Balanced Schemes on Simple Balance Laws written by Debora Amadori and published by Springer. This book was released on 2015-10-23 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents, in an attractive and self-contained form, techniques based on the L1 stability theory derived at the end of the 1990s by A. Bressan, T.-P. Liu and T. Yang that yield original error estimates for so-called well-balanced numerical schemes solving 1D hyperbolic systems of balance laws. Rigorous error estimates are presented for both scalar balance laws and a position-dependent relaxation system, in inertial approximation. Such estimates shed light on why those algorithms based on source terms handled like "local scatterers" can outperform other, more standard, numerical schemes. Two-dimensional Riemann problems for the linear wave equation are also solved, with discussion of the issues raised relating to the treatment of 2D balance laws. All of the material provided in this book is highly relevant for the understanding of well-balanced schemes and will contribute to future improvements.
Download or read book Anomalies in Partial Differential Equations written by Massimo Cicognani and published by Springer Nature. This book was released on 2021-02-03 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions contained in the volume, written by leading experts in their respective fields, are expanded versions of talks given at the INDAM Workshop "Anomalies in Partial Differential Equations" held in September 2019 at the Istituto Nazionale di Alta Matematica, Dipartimento di Matematica "Guido Castelnuovo", Università di Roma "La Sapienza". The volume contains results for well-posedness and local solvability for linear models with low regular coefficients. Moreover, nonlinear dispersive models (damped waves, p-evolution models) are discussed from the point of view of critical exponents, blow-up phenomena or decay estimates for Sobolev solutions. Some contributions are devoted to models from applications as traffic flows, Einstein-Euler systems or stochastic PDEs as well. Finally, several contributions from Harmonic and Time-Frequency Analysis, in which the authors are interested in the action of localizing operators or the description of wave front sets, complete the volume.
Download or read book The continuous dependence of solutions to the Cauchy problem d over dt A u B u reverse epsilon symbol function symbol on A and B and applications to partial differential equations written by Xiangsheng Xu and published by . This book was released on 1988 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt:
