Emerson Abreu, Everaldo Medeiros, Marcos Montenegro
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The effect of diffusions and sources on semilinear elliptic problems
This paper deals with properties of non-negative solutions of the boundary value problem in the presence of diffusion a and source f in a bounded domain Ω ⊂ Rn, n ≥ 1, where a and f are non-decreasing continuous functions on [0,L0) and f is positive. Part of the results are new even if we restrict ourselves to the Gelfand type case L0 = ∞, a(t) = t and f is a convex function. We study the behavior of related extremal parameters and solutions with respect to L0 and also to a and f in the C0 topology. The work is carried out in a unified framework for 0 < L0 ≤ ∞ under some interactive conditions between a and f.
期刊介绍:
ESAIM: COCV strives to publish rapidly and efficiently papers and surveys in the areas of Control, Optimisation and Calculus of Variations.
Articles may be theoretical, computational, or both, and they will cover contemporary subjects with impact in forefront technology, biosciences, materials science, computer vision, continuum physics, decision sciences and other allied disciplines.
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in control: modeling, controllability, optimal control, stabilization, control design, hybrid control, robustness analysis, numerical and computational methods for control, stochastic or deterministic, continuous or discrete control systems, finite-dimensional or infinite-dimensional control systems, geometric control, quantum control, game theory;
in optimisation: mathematical programming, large scale systems, stochastic optimisation, combinatorial optimisation, shape optimisation, convex or nonsmooth optimisation, inverse problems, interior point methods, duality methods, numerical methods, convergence and complexity, global optimisation, optimisation and dynamical systems, optimal transport, machine learning, image or signal analysis;
in calculus of variations: variational methods for differential equations and Hamiltonian systems, variational inequalities; semicontinuity and convergence, existence and regularity of minimizers and critical points of functionals, relaxation; geometric problems and the use and development of geometric measure theory tools; problems involving randomness; viscosity solutions; numerical methods; homogenization, multiscale and singular perturbation problems.