Trends in Nonlinear AnalysisMarkus Kirkilionis, Susanne Krömker, Rolf Rannacher, Friedrich Tomi Applied mathematics is a central connecting link between scientific observations and their theoretical interpretation. Nonlinear analysis has surely contributed major developments which nowadays shape the face of applied mathematics. At the beginning of the millennium, all sciences are expanding at increased speed. Technological, ecological, economical and medical problem solving is a central issue of every modern society. Mathematical models help to expose fundamental structures hidden in these problems and serve as unifying tools to deepen our understanding. What are the new challenges applied mathematics has to face with the increased diversity of scientific problems? In which direction should the classical tools of nonlinear analysis be developed further? How do new available technologies influence the development of the field? How can problems be solved which have been beyond reach in former times? It is the aim of this book to explore new developments in the field by way of discussion of selected topics from nonlinear analysis. |
Contents
| 1 | |
| 3 | |
| 6 | |
of ReactionDiffusion Patterns | 22 |
Sturm attractors and Sturm permutations | 34 |
Combinatorics of Sturm attractors | 41 |
References | 140 |
and Paraboliclike Evolutions | 153 |
References | 264 |
to Conformation Dynamics in Drug Design | 268 |
A Posteriori Error Estimates | 289 |
References | 305 |
References | 320 |
A Mathematical Birds Eye View | 322 |
References | 337 |
References | 373 |
Other editions - View all
Trends in Nonlinear Analysis Markus Kirkilionis,Susanne Krömker,Rolf Rannacher,Friedrich Tomi Limited preview - 2002 |
Trends in Nonlinear Analysis Markus Kirkilionis,Susanne Krömker,Rolf Rannacher,Friedrich Tomi No preview available - 2012 |
Trends in Nonlinear Analysis Markus Kirkilionis,Susanne Kromker,Rolf Rannacher No preview available - 2014 |
Common terms and phrases
analysis Archimedean spiral asymptotic boundary conditions bounded Cahn-Hilliard equation center manifold consider convergence convex corresponding curvature defined denote differential equations diffusion dispersion relation domain Dynamical Systems eigenfunctions eigenvalues equilibria essential spectrum evolution example existence exponential farfield filaments finite Floquet exponents flow fluid Fredholm index front function geometric global attractors gradient group velocity heteroclinic orbits Hopf bifurcation imaginary axis interface layer Lemma linear Lyapunov function Math mathematical meandering Morse Neumann boundary conditions nonlinear nonlocal parabolic equations parameter perturbation phase Phys point spectrum positive problem pulse radial reaction-diffusion system reflector rotating wave scalar scroll wave Section simulations singular space dimension spatial spec spiral waves stable Sturm attractors Sturm permutations Sturm property symmetric Theorem theory tion tip motion transverse travelling waves Turing pattern unique unstable manifolds vector wave solution wavetrains zero