The Surface Evaporation Problem with Signorini Boundary Condition

SUMMARYWe present a rigorous mathematical treatment of a model describing rain water infiltration through the vadose zone in case of runoff of the excess water. The main feature of the mathematical problem emerging from the model lies on the boundary condition on the ground surface which is in the form of a unilateral constraint. Existence and uniqueness of a weak solution is proved under general assumptions. We present also the results of a numerical study comparing the proposed model with other models which approach in a different way the rain water infiltration problem.

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“…To prove uniqueness, we are going to exploit the technique proposed in Reference [15]. We start by showing the following.…”

Section: Uniquenessmentioning

confidence: 99%

“…The additional condition (16) fills such a gap. In other words, in solving problem (P) one has to identify that particular selection of H such that both (15) and (16) (which is mass conservation) are fulfilled.…”

Section: Assumptions and Weak Solutionmentioning

confidence: 99%

A rain water infiltration model with unilateral boundary condition: qualitative analysis and numerical simulations

Borsi

Farína

Primicerio

2006

Math Methods in App Sciences

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“…Such a case has been studied in [12]. As before, x = 0 represents the impervious layer confining the bottom of the aquifer and x = 1 the ground surface.…”

Section: Assumptions and Basic Equationsmentioning

confidence: 99%

“…where q ≤ 0 is the evaporation rate. Actually, as pointed out in [12], the evaporation rate could not be prescribed, since, in general, q depends on u(1, t) as well as other physical parameters (e.g. temperature, wind velocity, relative humidity, etc.).…”

Section: Assumptions and Basic Equationsmentioning

confidence: 99%

Continuous dependence on the constitutive functions for a class of problems describing fluid flow in porous media

Borsi¹,

Farína²,

Gianni³

et al. 2009

Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur.

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In this paper we consider the PDE describing the fluid flow in a porous medium, focusing on the solution's dependence upon the choice of the saturation curve and the hydraulic conductivity. Basically, we consider two different saturation curves (say θ 1 and θ 2 ) and two different hydraulic conductivities (K 1 and K 2 ) which are both "close" in the L ∞ loc -norm. Then we find estimates to prove a constitutive stability for the solutions of the corresponding problems with the same boundary and initial conditions.

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Filtration in partially saturated and partially dried layered porous media

Xiao

Huang

1997

Acta Mathematicae Applicatae Sinica

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The Surface Evaporation Problem with Signorini Boundary Condition

Cited by 3 publications

References 6 publications

A rain water infiltration model with unilateral boundary condition: qualitative analysis and numerical simulations

A rain water infiltration model with unilateral boundary condition: qualitative analysis and numerical simulations

Continuous dependence on the constitutive functions for a class of problems describing fluid flow in porous media

Filtration in partially saturated and partially dried layered porous media

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