Trends in Nonlinear Analysis
Markus Kirkilionis, Susanne Krömker, Rolf Rannacher, Friedrich Tomi
Springer Science & Business Media, Apr 17, 2013 - Mathematics - 419 pages
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.
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analysis Archimedean spiral assume asymptotic boundary conditions bounded Cahn–Hilliard center manifold coefficients computed consider constant convergence convex corresponding curvature curve defined denote differential equations diffusion discrete dispersion relation domain eigenfunctions eigenvalues energy equilibria error estimates essential spectrum evolution example existence exponential farfield filaments finite Floquet exponents flow fluid Fredholm index front function geometric given gradient group velocity heteroclinic orbits homogeneous Hopf bifurcation imaginary axis instability interface Lemma limit linear Lyapunov function Math mathematical matrix meandering method Neumann boundary conditions nonlocal normal numerical parabolic equations parameter periodic orbit perturbation phase Phys point spectrum porous medium positive radial reaction-diffusion equations reaction-diffusion system rotating wave scalar scroll wave Section simulations singular space dimensions spatial spectral spiral waves stable Sturm attractors Sturm permutations Sturm property Theorem theory tion transverse travelling waves Turing pattern unique unstable manifolds vector wavetrains zero