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- W63873915 abstract "In this chapter, we discuss the control problem of the linear reaction-convectiondiffusion equation 4.1 $$frac{partial u}{partial t} = mu nabla^{2} u + nabla cdot (umathbf{v}) + au.$$ Depending on a particular real problem, u can represent a temperature or the concentration of a chemical species. The constant μ > 0 is the diffusivity of the temperature or the species, the vector v(x) = (v 1(x), …, vn(x)) is the velocity field of a fluid flow, and a(x) is a reaction rate. ∇2 is defined by $$nabla^{2} u = frac{partial^{2}u}{partial x_{1}^{2}} + ldots + frac{partial^{2} u}{partial x_{n}^{2}},$$ $$nabla u = left(frac{partial u}{partial x_{1}}, ldots, frac{partial u}{partial x_{n}}right).$$ $$nabla cdot (umathbf{v}) = {rm div} (umathbf{v}) = sumnolimits_{i = 1}^{n} frac{partial (uv_{i})}{partial x_{i}}$$ denotes the divergence of the vector u v." @default.
- W63873915 created "2016-06-24" @default.
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- W63873915 date "2009-11-22" @default.
- W63873915 modified "2023-10-03" @default.
- W63873915 title "Linear Reaction-Convection-Diffusion Equation" @default.
- W63873915 doi "https://doi.org/10.1007/978-3-642-04613-1_4" @default.
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