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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...
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...
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...
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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