Download Elliptic and Parabolic Problems: A Special Tribute to the by G. V. Caffarelli et al. PDF

By G. V. Caffarelli et al.

Haim Brezis has made major contributions within the fields of partial differential equations and practical research, and this quantity collects contributions through his former scholars and collaborators in honor of his sixtieth anniversary at a convention in Gaeta. It provides new advancements within the idea of partial differential equations with emphasis on elliptic and parabolic difficulties.

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Additional info for Elliptic and Parabolic Problems: A Special Tribute to the Work of Haim Brezis (Progress in Nonlinear Differential Equations and Their Applications)

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The obtained results show that global existence and nonexistence depend roughly on α, the degree of nonlinearity in f , the dimension n, and the size of the initial datum. In the early 70’s, Levine [8] introduced the concavity method and showed that solutions with negative energy blow-up in finite time. Later, this method had been improved by Kalantarov and Ladyzhenskaya [7] to accommodate more situations. Ball [2] also studied (1) with f depending on u as well as on ∇u and established a nonglobal existence result in n 44 S.

An iterative algorithm and numerical results are presented. 1. Introduction In many engineering applications involving high-temperature processes numerical simulation provides an insight into the radiative analysis of these complex systems and it promotes improvements of several process optimization (see [3, 5]). The motivation of this work is to compute the numerical solution of the problem addressed in [6] applied to a silicon purification process – see [1]. We consider, simultaneously, the phase change in the silicon and the non-local boundary condition arising from the Stefan-Boltzmann radiation condition at the enclosure surfaces within the ladle.

28 (1977), 473–486. , Kawohl B. , Gradient estimates for solutions of parabolic equations and systems, J. Math. Anal. Appl. 147 (1990), 309–329. , Blow-Up of solutions to quasilinear parabolic equations, Applied Math. Letters 12 (1999), 65–69. , Partial differential equations of parabolic type, Prentice-Hall Englewood NJ 1964. , Existence and nonexistence of solutions for ut = div(|∇u|p−2 ∇u) + f (∇u, u, x, t), J. Math. Anal. Appl. 172 (1993), 130–146. 50 S. A. K. , Formation of collapses in quasilinear equations of parabolic and hyperbolic types.

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