Metasolutions of Parabolic Equations in Population Dynamics by Julián López-Gómez download ebook FB2, MOBI
9781482238983 English 1482238985 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.", Metasolutions of Parabolic Equations in Population Dynamics is entirely devoted to the study of the effects of the spatial heterogeneities on the dynamics of large classes of parabolic equations of great interest in population dynamics. The book contains a series of optimal uniqueness results about large solutions of semilinear elliptic equations and provides non-uniqueness results for a general class of superlinear indefinite problems modeling the effects of strategic alliances in highly polluted environments. Each chapter includes a presentation of the problem, its mathematical formulation, the most important mathematical results available, and their proofs in a completely self-contained way.
9781482238983 English 1482238985 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.", Metasolutions of Parabolic Equations in Population Dynamics is entirely devoted to the study of the effects of the spatial heterogeneities on the dynamics of large classes of parabolic equations of great interest in population dynamics. The book contains a series of optimal uniqueness results about large solutions of semilinear elliptic equations and provides non-uniqueness results for a general class of superlinear indefinite problems modeling the effects of strategic alliances in highly polluted environments. Each chapter includes a presentation of the problem, its mathematical formulation, the most important mathematical results available, and their proofs in a completely self-contained way.