Fractal First-Order Partial Differential Equations

By Jérôme Droniou, C. Imbert. 2006

193 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/32c532f2549f1858d61d878be34458252f8f0c62

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In Applied Mathematics

In Modeling and Simulation

Citations in the corpus

Infinitely many solutions for impulsive fractional boundary value problem with p-Laplacian (2018, unknown): “14 ([33]) Assume that the functional Jλ defined above satisfies (A1) Jλ maps bounded sets into bounded sets uniformly for λ ∈ [1, 2], and Jλ(–u) = Jλ(u) for all (λ, u) ∈ [1, 2] × X ; (A2) B(u) ≥ 0 for all u ∈ X , A(u) → ∞ or B(u) → ∞ as ‖u‖ → ∞; or (A3) B(u) ≤ 0 for all u ∈ X , B(u) → –∞ as ‖u‖ → ∞;”
Estimates of Heat Kernel of Fractional Laplacian Perturbed by Gradient Operators (2007, methodology): “We like to note that our restriction to α> 1 is also adopted in [ 18 ] and [30] (see [6], too).”
On the differentiability of the solution to an equation with drift and fractional diffusion (2010, methodology): “It is used for example in [3], [13] and [9] for problems with drift and fractional diffusion.”
Entropy formulation for fractal conservation laws (2007, methodology): “Most of the studies (well-posedness, asymptotic behaviour, etc) are concerned with the range of exponent λ ∈]1, 2] (see [1, 2, 7, 6, 8 , 10]).”
Regularity results for nonlocal parabolic equations (2013, result): “1) (similar to the equation treated by Silvestre), Droniou and Imbert in [24] and Imbert in [33] study regularity properties and deduce classical solutions in many situations.”
On the differentiability of the solution to the Hamilton–Jacobi equation with critical fractional diffusion (2009, background): “This was proved in [9] and [8] for (1.”