By Isabel Narra Figueiredo, Lisa Santos
This publication gathers a set of refereed articles containing unique effects reporting the hot contributions of the lectures and communications offered on the unfastened Boundary difficulties convention that happened on the collage of Coimbra, Portugal, from June 7 to twelve, 2005 (FBP2005). They take care of the maths of a extensive category of versions and difficulties regarding nonlinear partial differential equations coming up in physics, engineering, biology and finance. one of the major subject matters, the talks thought of loose boundary difficulties in biomedicine, in porous media, in thermodynamic modeling, in fluid mechanics, in photo processing, in monetary arithmetic or in computations for inter-scale difficulties. The mathematical research and superb homes of strategies and interfaces in unfastened boundary difficulties were an lively topic within the final 3 many years and their mathematical figuring out remains to be an immense interdisciplinary software for the medical purposes, on one hand, and an intrinsic point of the present improvement of numerous vital mathematical disciplines.
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Extra info for Free Boundary Problems: Theory and Applications
Shmarev Abstract. We study the Dirichlet problem for a class of nonlinear parabolic equations with nonstandard anisotropic growth conditions. Equations of this class generalize the evolutional p(x, t)-Laplacian equation. We prove the existence of a bounded weak solution and study its localization (vanishing) properties. Mathematics Subject Classiﬁcation (2000). 35K55; 35K65. Keywords. Nonlinear parabolic equation, nonstandard growth conditions, anisotropic nonlinearity, localization of solutions.
V´azquez, An L1 -theory of existence and uniqueness of solutions of nonlinear elliptic equations. Ann. Scuola Norm. Sup. Pisa Cl. , 22(2) (1995), 241–273.  Ph. G. Crandall and A. Pazy, Evolution Equations Governed by Accretive Operators. Book to appear.  Ph. G. Crandall and P. Sacks, Some L1 existence and dependence results for semilinear elliptic equations under nonlinear boundary conditions. Appl. Math. , 17 (1986), 203–224.  Ph. B´enilan and P. Wittbold, On mild and weak solutions of elliptic-parabolic problems.
10) for some positive constants C, ν, tg and where u+ = max (0, u). Notice the constants δ1 , . . 8) are non-negative and, thus, only one component of the vector ﬁeld (δ1 |u1 |σ1 −2 u1 , . . 10) can be zero. 10). This feedback is presented as an anisotropic condition, because the dependence of f on u may be diﬀerent for distinct directions. 8), we can say the feedback forces ﬁeld h, and thus f , is dissipative, in order to each component uk , in all directions xk where δk > 0, for k = 1, .
Free Boundary Problems: Theory and Applications by Isabel Narra Figueiredo, Lisa Santos
Categories: Differential Equations