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Ordinary differential equations --- Differential geometry. Global analysis --- Evolution equations. --- Cauchy problem. --- Bifurcation theory. --- Differential equations, Parabolic. --- Equations d'évolution --- Cauchy, Problème de --- Théorie de la bifurcation --- Equations différentielles paraboliques --- 51 <082.1> --- Mathematics--Series --- Equations d'évolution --- Cauchy, Problème de --- Théorie de la bifurcation --- Equations différentielles paraboliques --- Bifurcation theory --- Cauchy problem --- Differential equations, Parabolic --- Evolution equations --- Evolutionary equations --- Equations, Evolution --- Equations of evolution --- Differential equations --- Parabolic differential equations --- Parabolic partial differential equations --- Differential equations, Partial --- Differential equations, Nonlinear --- Stability --- Numerical solutions --- Équations d'évolution. --- Équations différentielles paraboliques. --- Bifurcation, Théorie de la. --- Systèmes dynamiques
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Several types of differential equations, such as functional differential equation, age-structured models, transport equations, reaction-diffusion equations, and partial differential equations with delay, can be formulated as abstract Cauchy problems with non-dense domain. This monograph provides a self-contained and comprehensive presentation of the fundamental theory of non-densely defined semilinear Cauchy problems and their applications. Starting from the classical Hille-Yosida theorem, semigroup method, and spectral theory, this monograph introduces the abstract Cauchy problems with non-dense domain, integrated semigroups, the existence of integrated solutions, positivity of solutions, Lipschitz perturbation, differentiability of solutions with respect to the state variable, and time differentiability of solutions. Combining the functional analysis method and bifurcation approach in dynamical systems, then the nonlinear dynamics such as the stability of equilibria, center manifold theory, Hopf bifurcation, and normal form theory are established for abstract Cauchy problems with non-dense domain. Finally applications to functional differential equations, age-structured models, and parabolic equations are presented. This monograph will be very valuable for graduate students and researchers in the fields of abstract Cauchy problems, infinite dimensional dynamical systems, and their applications in biological, chemical, medical, and physical problems.
Evolution equations. --- Differential equations, Parabolic. --- Parabolic differential equations --- Parabolic partial differential equations --- Differential equations, Partial --- Evolutionary equations --- Equations, Evolution --- Equations of evolution --- Differential equations --- Differential Equations. --- Differential equations, partial. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Partial differential equations --- 517.91 Differential equations --- Differential equations. --- Partial differential equations.
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This book consists of six chapters written by leading researchers in mathematical biology. These chapters present recent and important developments in the study of structured population models in biology and epidemiology. Topics include population models structured by age, size, and spatial position; size-structured models for metapopulations, macroparasitc diseases, and prion proliferation; models for transmission of microparasites between host populations living on non-coincident spatial domains; spatiotemporal patterns of disease spread; method of aggregation of variables in population dynamics; and biofilm models. It is suitable as a textbook for a mathematical biology course or a summer school at the advanced undergraduate and graduate level. It can also serve as a reference book for researchers looking for either interesting and specific problems to work on or useful techniques and discussions of some particular problems.
Partial differential equations --- Differential equations --- Mathematics --- Biomathematics. Biometry. Biostatistics --- differentiaalvergelijkingen --- toegepaste wiskunde --- biomathematica --- biometrie
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Several types of differential equations, such as functional differential equation, age-structured models, transport equations, reaction-diffusion equations, and partial differential equations with delay, can be formulated as abstract Cauchy problems with non-dense domain. This monograph provides a self-contained and comprehensive presentation of the fundamental theory of non-densely defined semilinear Cauchy problems and their applications. Starting from the classical Hille-Yosida theorem, semigroup method, and spectral theory, this monograph introduces the abstract Cauchy problems with non-dense domain, integrated semigroups, the existence of integrated solutions, positivity of solutions, Lipschitz perturbation, differentiability of solutions with respect to the state variable, and time differentiability of solutions. Combining the functional analysis method and bifurcation approach in dynamical systems, then the nonlinear dynamics such as the stability of equilibria, center manifold theory, Hopf bifurcation, and normal form theory are established for abstract Cauchy problems with non-dense domain. Finally applications to functional differential equations, age-structured models, and parabolic equations are presented. This monograph will be very valuable for graduate students and researchers in the fields of abstract Cauchy problems, infinite dimensional dynamical systems, and their applications in biological, chemical, medical, and physical problems.
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This book consists of six chapters written by leading researchers in mathematical biology. These chapters present recent and important developments in the study of structured population models in biology and epidemiology. Topics include population models structured by age, size, and spatial position; size-structured models for metapopulations, macroparasitc diseases, and prion proliferation; models for transmission of microparasites between host populations living on non-coincident spatial domains; spatiotemporal patterns of disease spread; method of aggregation of variables in population dynamics; and biofilm models. It is suitable as a textbook for a mathematical biology course or a summer school at the advanced undergraduate and graduate level. It can also serve as a reference book for researchers looking for either interesting and specific problems to work on or useful techniques and discussions of some particular problems.
Population biology --- Biologie des populations --- Mathematical models. --- Modèles mathématiques --- Epidemiology --- Population Dynamics --- Models, Theoretical --- Biology --- Epidemiologic Methods --- Public Health --- Investigative Techniques --- Demography --- Biological Science Disciplines --- Epidemiologic Measurements --- Population Characteristics --- Natural Science Disciplines --- Analytical, Diagnostic and Therapeutic Techniques and Equipment --- Social Sciences --- Environment and Public Health --- Health Care --- Anthropology, Education, Sociology and Social Phenomena --- Disciplines and Occupations --- Biology - General --- Calculus --- Mathematics --- Health & Biological Sciences --- Physical Sciences & Mathematics --- Mathematical models --- Methodology --- Research --- Methodology. --- Mathematics. --- Differential equations. --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Biomathematics. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Mathematical and Computational Biology. --- Applications of Mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Partial differential equations --- 517.91 Differential equations --- Differential equations --- Math --- Science --- Differential Equations. --- Differential equations, partial.
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This book consists of six chapters written by leading researchers in mathematical biology. These chapters present recent and important developments in the study of structured population models in biology and epidemiology. Topics include population models structured by age, size, and spatial position; size-structured models for metapopulations, macroparasitc diseases, and prion proliferation; models for transmission of microparasites between host populations living on non-coincident spatial domains; spatiotemporal patterns of disease spread; method of aggregation of variables in population dynamics; and biofilm models. It is suitable as a textbook for a mathematical biology course or a summer school at the advanced undergraduate and graduate level. It can also serve as a reference book for researchers looking for either interesting and specific problems to work on or useful techniques and discussions of some particular problems.
Partial differential equations --- Differential equations --- Mathematics --- Biomathematics. Biometry. Biostatistics --- differentiaalvergelijkingen --- toegepaste wiskunde --- biomathematica --- biometrie
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General ecology and biosociology --- Spatial ecology --- Mathematical models
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