1,721,009 research outputs found
Nonlinear transmission problems for quasilinear diffusion systems} Netw. Heterog. Media
No full textWe study degenerate quasilinear parabolic systems in two different domains, which are connected by a nonlinear transmission condition at their interface. For a large class of models, including those modeling pollution aggression on stones and chemotactic movements of bacteria, we prove global existence, uniqueness and stability of the solutions
Global existence and uniqueness of solutions for multidimensional weakly parabolic systems arising in chemistry and biology
No full textIn this paper we establish general well-posedeness results for a
wide class of weakly parabolic 2 × 2 systems in a bounded domain of RN . Our
results cover examples arising in sulphation of marbles and chemotaxis, when
the density of one chemical component is not diffusing. We show that, under
quite general assumptions, uniform L∞ estimates are sufficient to establish the
global existence and stability of solutions, even if in general the nonlinear terms
in the equations depend also on the gradient of the solutions. Applications are
presented and discussed
Global existence of solutions to a nonlinear model of sulphation phenomena in calcium carbonate stones
No full textWe prove global existence and uniqueness of smooth solutions to a nonlinear system of parabolic equations, which arises to describe the evolution of the chemical aggression due to the action of sulphur dioxide on calcium carbonate stones. This system is not strongly parabolic and only some energy estimates are available. Nevertheless, global (in time) results are proven using a weak continuation principle for the local solutions. (c) 2004 Elsevier Ltd. All rights reserved
Chemomechanical Degradation of Monumental Stones: Preliminary Results
No full textThe degradation of monumental stones resulting from the mutual interaction between mechanical actions and environment/pollution conditions is investigated here. In particular, the stone degradation is estimated as a function of the environmental conditions and the prediction of damaging phenomena, which can compromise permanently the fruition of monuments. This is done through a macroscopic phenomenological model which accounts for the main aspects of the problem: the chemical reaction and the mechanical behavior of stones. The sulphation reaction and the diffusion of the pollutant agents are described by suitable differential equations coupled with a variational formulation of fracture mechanics. The proposed model permits to evaluate how much aggressive atmospheric agents contribute to the decay of the mechanical properties of the stones as well as to establish the impact of the synergic chemical aggression and stress state. The latter is also influenced by the chemical reaction and by the evolving mechanical properties of the material. The main features of this approach are illustrated by specific numerical simulations
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