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| Author | : Lawrence C. Evans |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 98 |
| Release | : 1990 |
| Genre | : Mathematics |
| ISBN | : 0821807242 |
"Expository lectures from the the CBMS Regional Conference held at Loyola University of Chicago, June 27-July 1, 1988."--T.p. verso.
| Author | : Lawrence C. Evans |
| Publisher | : |
| Total Pages | : 82 |
| Release | : 2020 |
| Genre | : Convergence |
| ISBN | : 9787040534993 |
| Author | : V. Lakshmikantham |
| Publisher | : CRC Press |
| Total Pages | : 328 |
| Release | : 2003-02-27 |
| Genre | : Mathematics |
| ISBN | : 1482288273 |
A monotone iterative technique is used to obtain monotone approximate solutions that converge to the solution of nonlinear problems of partial differential equations of elliptic, parabolic and hyperbolic type. This volume describes that technique, which has played a valuable role in unifying a variety of nonlinear problems, particularly when combin
| Author | : Sören Bartels |
| Publisher | : Springer |
| Total Pages | : 394 |
| Release | : 2015-01-19 |
| Genre | : Mathematics |
| ISBN | : 3319137972 |
The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.
| Author | : Yuxi Zheng |
| Publisher | : |
| Total Pages | : 150 |
| Release | : 1990 |
| Genre | : |
| ISBN | : |
| Author | : Tomás Roubicek |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 415 |
| Release | : 2006-01-17 |
| Genre | : Mathematics |
| ISBN | : 3764373970 |
This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition quickly leads general theory to analysis of concrete equations, which have specific applications in such areas as electrically (semi-) conductive media, modeling of biological systems, and mechanical engineering. Methods of Galerkin or of Rothe are exposed in a large generality.
| Author | : Mi-Ho Giga |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 307 |
| Release | : 2010-05-30 |
| Genre | : Mathematics |
| ISBN | : 0817646515 |
This work will serve as an excellent first course in modern analysis. The main focus is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. This textbook will be an excellent resource for self-study or classroom use.
| Author | : Denis Talay |
| Publisher | : Springer |
| Total Pages | : 312 |
| Release | : 2006-11-13 |
| Genre | : Mathematics |
| ISBN | : 3540685138 |
The lecture courses of the CIME Summer School on Probabilistic Models for Nonlinear PDE's and their Numerical Applications (April 1995) had a three-fold emphasis: first, on the weak convergence of stochastic integrals; second, on the probabilistic interpretation and the particle approximation of equations coming from Physics (conservation laws, Boltzmann-like and Navier-Stokes equations); third, on the modelling of networks by interacting particle systems. This book, collecting the notes of these courses, will be useful to probabilists working on stochastic particle methods and on the approximation of SPDEs, in particular, to PhD students and young researchers.
| Author | : Michael Struwe |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 256 |
| Release | : 2013-04-17 |
| Genre | : Science |
| ISBN | : 3662026244 |
It would be hopeless to attempt to give a complete account of the history of the calculus of variations. The interest of Greek philosophers in isoperimetric problems underscores the importance of "optimal form" in ancient cultures, see Hildebrandt-Tromba [1] for a beautiful treatise of this subject. While variatio nal problems thus are part of our classical cultural heritage, the first modern treatment of a variational problem is attributed to Fermat (see Goldstine [1; p.l]). Postulating that light follows a path of least possible time, in 1662 Fer mat was able to derive the laws of refraction, thereby using methods which may already be termed analytic. With the development of the Calculus by Newton and Leibniz, the basis was laid for a more systematic development of the calculus of variations. The brothers Johann and Jakob Bernoulli and Johann's student Leonhard Euler, all from the city of Basel in Switzerland, were to become the "founding fathers" (Hildebrandt-Tromba [1; p.21]) of this new discipline. In 1743 Euler [1] sub mitted "A method for finding curves enjoying certain maximum or minimum properties", published 1744, the first textbook on the calculus of variations.
| Author | : E.E. Rosinger |
| Publisher | : Elsevier |
| Total Pages | : 429 |
| Release | : 1987-11-01 |
| Genre | : Science |
| ISBN | : 0080872573 |
During the last few years, several fairly systematic nonlinear theories of generalized solutions of rather arbitrary nonlinear partial differential equations have emerged. The aim of this volume is to offer the reader a sufficiently detailed introduction to two of these recent nonlinear theories which have so far contributed most to the study of generalized solutions of nonlinear partial differential equations, bringing the reader to the level of ongoing research.The essence of the two nonlinear theories presented in this volume is the observation that much of the mathematics concerning existence, uniqueness regularity, etc., of generalized solutions for nonlinear partial differential equations can be reduced to elementary calculus in Euclidean spaces, combined with elementary algebra in quotient rings of families of smooth functions on Euclidean spaces, all of that joined by certain asymptotic interpretations. In this way, one avoids the complexities and difficulties of the customary functional analytic methods which would involve sophisticated topologies on various function spaces. The result is a rather elementary yet powerful and far-reaching method which can, among others, give generalized solutions to linear and nonlinear partial differential equations previously unsolved or even unsolvable within distributions or hyperfunctions.Part 1 of the volume discusses the basic limitations of the linear theory of distributions when dealing with linear or nonlinear partial differential equations, particularly the impossibility and degeneracy results. Part 2 examines the way Colombeau constructs a nonlinear theory of generalized functions and then succeeds in proving quite impressive existence, uniqueness, regularity, etc., results concerning generalized solutions of large classes of linear and nonlinear partial differential equations. Finally, Part 3 is a short presentation of the nonlinear theory of Rosinger, showing its connections with Colombeau's theory, which it contains as a particular case.
