Metasolutions of parabolic equations in population dynamics
- Boca Raton : CRC Press, 2016
- xviii, 357 p. ; ill. , 24 cm
Includes bibliographical references and index.
Analyze Global Nonlinear Problems Using Metasolutions Metasolutions of Parabolic Equations in Population Dynamics explores the dynamics of a generalized prototype of semilinear parabolic logistic problem. Highlighting the author's advanced work in the field, it covers the latest developments in the theory of nonlinear parabolic problems. The book reveals how to mathematically determine if a species maintains, dwindles, or increases under certain circumstances. It explains how to predict the time evolution of species inhabiting regions governed by either logistic growth or exponential growth. The book studies the possibility that the species grows according to the Malthus law while it simultaneously inherits a limited growth in other regions. The first part of the book introduces large solutions and metasolutions in the context of population dynamics. In a self-contained way, the second part analyzes a series of very sharp optimal uniqueness results found by the author and his colleagues. The last part reinforces the evidence that metasolutions are also categorical imperatives to describe the dynamics of huge classes of spatially heterogeneous semilinear parabolic problems. Each chapter presents the mathematical formulation of the problem, the most important mathematical results available, and proofs of theorems where relevant.
9781482238983
Differential equations Parabolic Asymptotically stable Bifurcation diagram Boundary value problem Compact subsets Dirichlet boundary conditions Global bifurcation Harnack inequality Logistic equation Maximum principle Unique positive solution Unstable manifolds