Download or read book Nonlinear Systems of Partial Differential Equations written by Anthony W. Leung and published by World Scientific Publishing Company. This book was released on 2009 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Positive solutions for systems of two equations. 1.1. Introduction. 1.2. Strictly positive coexistence for diffusive prey-predator systems. 1.3. Strictly positive coexistence for diffusive competing systems. 1.4. Strictly positive coexistence for diffusive cooperating systems. 1.5. Stability of steady-states as time changes -- 2. Positive solutions for large systems of equations. 2.1. Introduction. 2.2. Synthesizing large (biological) diffusive systems from smaller subsystems. 2.3. Application to epidemics of many interacting infected species. 2.4. Conditions for coexistence in terms of signs of principal eigenvalues of related single equations, mixed boundary data. 2.5. Positive steady-states for large systems by index method. 2.6. Application to reactor dynamics with temperature feedback -- 3. Optimal control for nonlinear systems of partial differential equations. 3.1. Introduction and preliminary results for scalar equations. 3.2. Optimal harvesting-coefficient control of steady-state prey-predator diffusive Volterra-Lotka systems. 3.3. Time-periodic optimal control for competing parabolic systems. 3.4. Optimal control of an initial-boundary value problem for fission reactor systems. 3.5. Optimal boundary control of a parabolic problem -- 4. Persistence, upper and lower estimates, blowup, cross-diffusion and degeneracy. 4.1. Persistence. 4.2. Upper-lower estimates, attractor set, blowup. 4.3. Diffusion, self and cross-diffusion with no-flux boundary condition. 4.4. Degenerate and density-dependent diffusions, non-extinction in highly spatially heterogenous environments -- 5. Traveling waves, systems of waves, invariant manifolds, fluids and plasma. 5.1. Traveling wave solutions for competitive and monotone systems. 5.2. Positive solutions for systems of wave equations and their stabilities. 5.3. Invariant manifolds for coupled Navier-stokes and second order wave equations. 5.4. Existence and global bounds for fluid equations of plasma display technology