A non-local regularization of first order Hamilton–Jacobi equations

By C. Imbert. 2005

99 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/ff9701cf02eaf684cac45e176cc24a01ba7db1c6

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In Applied Mathematics

In Modeling and Simulation

Citations in the corpus

On the strong maximum principle for second order nonlinear parabolic integro-differential equations (2010, methodology): “The notion of viscosity solution generalizes the one introduced by Imbert in [16] for first-order Hamilton Jacobi equations in the whole space and Arisawa in [3], [4] for degenerate integro-differential equations on bounded domains.”
Second-order elliptic integro-differential equations: viscosity solutions' theory revisited (2007, background): “3 An additional proposition In [11], general test-functions are replaced with functions φ(t, x) = αt + p · x ± σ|x|2 + o(|t| + |x|2).”
A Widder’s Type Theorem for the Heat Equation with Nonlocal Diffusion (2013, background): “See [6] for more details about these type of solutions.”
Well-posedness of Hamilton–Jacobi equations with Caputo’s time fractional derivative (2016, background): “See also [5], [2], [6], [17] and references therein.”
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.”
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 Dirichlet Problem for Second-Order Elliptic Integro-Differential Equations (2008, background): “[9,14] for local equations and [19,1,4,5,13] for non-local ones) together with the comparison result of [4] provides the existence of a solution u for this integro-differential equation such that |u| ≤M.”
Entropy formulation for fractal conservation laws (2007, methodology): “1), we have used an integral formula for g (see papers of Imbert [9] and of Droniou and Imbert [8] or Theorem 2.”