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- W202295475 abstract "Publisher Summary This chapter discusses some existence and stability results for solutions of reaction–diffusion systems with nonlinear boundary conditions. By using a result of H. Brezis and an elementary comparison argument, the elliptic problem is reduced to an application of Schauders fixed point theorem. This gives the existence of a weak solution and a regularity argument shows that it is in fact a classical solution. The chapter presents an example arising in combustion theory. The chapter presents a proof of uniqueness and global stability for solutions of the elliptic system if, the Lipschitz constants of f and g are small. This gives an elementary proof of results in a more general setting. Existence for the elliptic problem was obtained by using differential inequalities. The chapter discusses the case of nonlinearities depending on the gradient and presents its proof. The existence of maximal and minimal solutions for the combustion system is proved by finding a monotone scheme involving the growth properties of the nonlinear terms." @default.
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- W202295475 date "1981-01-01" @default.
- W202295475 modified "2023-10-17" @default.
- W202295475 title "SOME EXISTENCE AND STABILITY RESULTS FOR SOLUTIONS OF REACTION-DIFFUSION SYSTEMS WITH NONLINEAR BOUNDARY CONDITIONS" @default.
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- W202295475 doi "https://doi.org/10.1016/b978-0-12-508780-3.50019-5" @default.
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