Author | Wu, Jianhong. author |
---|---|
Title | Theory and Applications of Partial Functional Differential Equations [electronic resource] / by Jianhong Wu |
Imprint | New York, NY : Springer New York, 1996 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4050-1 |
Descript | X, 432 p. online resource |
1. Preliminaries -- 1.1 Semigroups and generators -- 1.2 Function spaces, elliptic operators, and maximal principles -- Bibliographical Notes -- 2. Existence and Compactness of Solution Semiflows -- 2.1 Existence and compactness -- 2.2 Local existence and global continuation -- 2.3 Extensions to neutral partial functional differential equations -- Bibliographical Notes -- 3. Generators and Decomposition of State Spaces for Linear Systems -- 3.1 Infinitesimal generators of solution semiflows of linear systems -- 3.2 Decomposition of state spaces by invariant subspaces -- 3.3 Computation of center, stable, and unstable subspaces -- 3.4 Extensions to equations with infinite delay -- 3.5 L2-stability and reduction of neutral equations -- Bibliographical Notes -- 4. Nonhomogeneous Systems and Linearized Stability -- 4.1 Dual operators and an alternative theorem -- 4.2 Variation of constants formula -- 4.3 Existence of periodic or almost periodic solutions -- 4.4 Principle of linearized stability -- 4.5 Fundamental transformations and representations of solutions -- Bibliographical Notes -- 5. Invariant Manifolds of Nonlinear Systems -- 5.1 Stable and unstable manifolds -- 5.2 Center manifolds -- 5.3 Flows on center manifolds -- 5.4 Global invariant manifolds of perturbed wave equations -- Bibliographical Notes -- 6. Hopf Bifurcations -- 6.1 Some classical Hopf bifurcation theorems for ODEs -- 6.2 Smooth local Hopf bifurcations: a special case -- 6.3 Some examples from population dynamics -- 6.4 Smooth local Hopf bifurcations: general situations -- 6.5 A topological global Hopf bifurcation theory -- 6.6 Global continuation of wave solutions -- Bibliographical Notes -- 7. Small and Large Diffusivity -- 7.1 Destablization of periodic solutions by small diffusivity -- 7.2 Large diffusivity under Neumann boundary conditions -- Bibliographical Notes -- 8. Invariance, Comparison, and Upper and Lower Solutions -- 8.1 Invariance and inequalities -- 8.2 Systems and strict inequalities -- 8.3 Applications to reaction diffusion equations with delay -- Bibliographical Notes -- 9. Convergence, Monotonicity, and Contracting Rectangles -- 9.1 Monotonicity and generic convergence -- 9.2 Stability and steady state solutions of quasimonotone systems -- 9.3 Comparison and convergence results -- 9.4 Applications to Lotka-Volterra competition models -- Bibliographical Notes -- 10. Dispativeness, Exponential Growth, and Invariance Principles -- 10.1 Point dispativeness in a scalar equation -- 10.2 Convergence in a scalar equation -- 10.3 Exponential growth in a scalar equation -- 10.4 An invariance principle -- Bibliographical Notes -- 11. Traveling Wave Solutions -- 11.1 Huxley nonlinearities and phase plane arguments -- 11.2 Delayed Fisher equation: sub-super solution method -- 11.3 Systems and monotone iteration method -- 11.4 Traveling oscillatory waves -- Bibliographical Notes