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Record Nr. |
UNINA9910816632303321 |
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Autore |
Leung Anthony W. <1946-> |
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Titolo |
Nonlinear systems of partial differential equations : applications to life and physical sciences / / Anthony W. Leung |
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Pubbl/distr/stampa |
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Hackensack, N.J., : World Scientific, c2009 |
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ISBN |
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1-282-75835-7 |
9786612758355 |
981-4277-70-3 |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (xii, 532 p. ) : ill |
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Classificazione |
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Disciplina |
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Soggetti |
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Differential equations, Partial |
Differential equations, Nonlinear |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Positive solutions for systems of two equations -- Positive solutions for large systems of equations -- Optimal control for nonlinear systems of partial differential equations -- Persistence, upper and lower estimates, blowup, cross-diffusion and degeneracy -- Traveling waves, systems of waves, invariant manifolds, fluids and plasma -- Appendices. |
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Sommario/riassunto |
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The book presents the theory of diffusion-reaction equations starting from the Volterra-Lotka systems developed in the eighties for Dirichlet boundary conditions. It uses the analysis of applicable systems of partial differential equations as a starting point for studying upper-lower solutions, bifurcation, degree theory and other nonlinear methods. It also illustrates the use of semigroup, stability theorems and W2ptheory. Introductory explanations are included in the appendices for non-expert readers. The first chapter covers a wide range of steady-state and stability results involving prey-predator, competing and cooperating species under strong or weak interactions. Many diagrams are included to easily understand the description of the range of parameters for coexistence. The book provides a comprehensive presentation of topics developed by numerous researchers. Large complex systems are introduced for modern research in ecology, medicine and engineering. Chapter 3 combines the |
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theories of earlier chapters with the optimal control of systems involving resource management and fission reactors. This is the first book to present such topics at research level. Chapter 4 considers persistence, cross-diffusion, and boundary induced blow-up, etc. The book also covers traveling or systems of waves, coupled Navier-Stokes and Maxwell systems, and fluid equations of plasma display. These should be of interest to life and physical scientists. |
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