Free Boundary Problems by Isabel Narra Figueiredo, Isabel N. Figueiredo;José F. PDF

By Isabel Narra Figueiredo, Isabel N. Figueiredo;José F. Rodrigues;Lisa Santos

ISBN-10: 3764377186

ISBN-13: 9783764377182

ISBN-10: 3764377194

ISBN-13: 9783764377199

This ebook gathers a set of refereed articles containing unique effects reporting the new contributions of the lectures and communications provided on the loose Boundary difficulties convention that happened on the collage of Coimbra, Portugal, from June 7 to twelve, 2005 (FBP2005). They care for the math of a large classification of versions and difficulties concerning nonlinear partial differential equations bobbing 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 picture processing, in monetary arithmetic or in computations for inter-scale problems.

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Example text

Finally, for S = −pI + 2µD + (q−2)/2 D and q ≥ 2, the existence of a weak solution was also proved in [7]. 2), repeating the corresponding arguments of [6, 7] (see also [8, 10]) and to use a fixed point argument. We hope to publish these results elsewhere as soon as possible. 5), every weak solution satisfies N δ |∇u|q + Ω δi |ui |σi i=1 dx ∈ L1 [0, T ]. 28 S. B. 2. 8) and exhibits dissipation effect in one direction. e. 8) holds with δN = 0 and δj = 0 for all j = N . 6) Let us consider the following hypothesis on the domain Ω.

Antontsev and S. Shmarev − ± − − with given finite constants p± i , σ , pi > 1, p > 1, σ > 1. a. z ∈ Q), 0 < a0 ≤ ai (z, r) ≤ a1 < ∞, 0 ≤ c0 ≤ c(z, u) ≤ c1 < ∞, a0 , a1 , c0 , c1 = const . 4) i where ω(τ ) is continuous for τ > 0 and lim ω(τ ) ln τ →0+ 1 = C < +∞. 1) which degenerates if |Di u|pi (z) = 0 or becomes singular if |Di u|pi (z) = ∞. 1) belong to. 1) and give a sketch of proofs. 1) either identically vanish in a finite time (if p+ < 2), or possess the property of finite speed of propagation of disturbances from the initial data (if p− > 2).

On Q. 15) 0 for all s ∈ [0, T ], where 1 |θλ |2H 1 (Ω) − (h, −∆0 θλ )L2 (Ω) + | − ∆0 wλ + βλ (wλ )|2L2 (Ω) 2 −2(−∆0 wλ + βλ (wλ ), f (θλ , wλ ))L2 (Ω) , 1 1 |θ |2 2 Gλ (·) := + |∇θλ |2L2 (Ω) + ϕ(wλ ). 4 λ L (Ω) 2 ˜λ is uniformly ˜λ (0)}λ∈(0,1] is bounded, this inequality implies that E Since {E bounded on [0, T ] with respect to λ ∈ (0, 1]. 15) we have an inequality which is required in the lemma. E˜λ (·) := 4. 1. 3 holds, and put ξλ := −wλ + ∆0 wλ − βλ (wλ ) + f (θλ , wλ ) again. 11) we can choose a sequence {λn } ⊂ (0, 1] tending to 0 as n → ∞ with functions θ, w ∈ W 1,2 (0, T ; H 1(Ω)) ∩ L∞ (0, T ; H 2 (Ω)) and ξ, η ∈ L∞ (0, T ; L2(Ω)) such that θn := θλn → θ, wn := wλn → w in C([0, T ]; H 1 (Ω)) as n → ∞.

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Free Boundary Problems by Isabel Narra Figueiredo, Isabel N. Figueiredo;José F. Rodrigues;Lisa Santos


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