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If Ω is a bounded domain in R N and f a continuous nondecreasing function satisfying a super linear growth condition at infinity, we study the existence and uniqueness of solutions for the problem (P): ∂tu−Δu+f(u)=0 in Q∞ Ω :=Ω×(0,∞), u=∞ on the parabolic boundary ∂pQ. We prove...
For 1-D linear hyperbolic systems with constant coefficients we introduce the asymptotic controllability and the asymptotic zero controllability in L 2 space under the lack of boundary controls and show the duality that they are equivalent, respectively, to the strong observability and the weak...
Let A be a 2mth-order elliptic operator in divergence form subject to the Dirichlet boundary conditions in a bounded C ρ domain Ω of R n , whose coefficients are in C σ with given σ>0, where ρ=1 if 0<σ≤1 and ρ=σ+1 if σ>1. Then we investigate the asymptotic formula for the partition...
We discuss the grazing collision limit of certain kinetic models of Bose–Einstein particles obtained from a suitable modification of the one-dimensional Kac caricature of a Maxwellian gas without cut-off. We recover in the limit a non-linear Fokker–Planck equation which presents many...
A lower semicontinuity result is proved in the space of special vector fields with bounded deformation for a fracture energetic model of the type ∫JuΨ((u), νu) dℋ N−1 , (u)·νu≥0, ℋ N−1 -a.e. on Ju. A representation of the energy density Ψ, which ensures lower semicontinuity, is...
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