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Spatiotemporal patterns near a codimension-2 Turing-Hopf point of the one-dimensional
superdiffusive Brusselator model are analyzed. The superdiffusive Brusselator model
differs from its regular counterpart in that the Laplacian operator of the regular model
is replaced by ∂α/∂|ξ|α, 1 < α
< 2, an integro-differential operator that reflects the nonlocal behavior of
superdiffusion. The order of the operator, α, is a measure of the rate of
...
We study the properties of interfaces in solutions of the Cauchy problem for the nonlinear degenerate parabolic equation ut = Δum - up in Rn x (0,T] with the parameters m > 1, p > 0 satisfying the condition m + p ≥ 2. We show that the velocity of the interface Γ(t) = ∂{supp u(x,t)} is given by the formula v = [ -m / (m-1) ∇um-1 + ∇Π ]|Γ(t) where Π is the solution of the degenerate elliptic equation div (u∇Π) + up = 0, Π = 0 on Γ(t). We give explicit formulas which represent the interface...
Abbiamo considerato il problema della regolarità interna delle soluzioni deboli della seguente equazione differenziale dove , ed per . I nostri principali risultati sono una stima a priori interna del tipo e la regolarità hölderiana di . La stima a priori delle derivate viene ottenuta utilizzando una tecnica analoga a quella introdotta da Chiarenza, Frasca e Longo in [3], per gli operatori ellittici in forma di non divergenza, supponendo che i coefficienti verifichino una condizione...
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