Continuity of the temperature in boundary heat control problems

By I. Athanasopoulos, Luis Caffarelli. 2010

68 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/10b1f60c66d4eaa3fcfe8388b78bdfefd86bd9c2

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Citations in the corpus

A Priori Estimates for Fractional Nonlinear Degenerate Diffusion Equations on Bounded Domains (2013, background): “We refer to [1, 11, 10, 38, 39] for the physical motivation and relevance of this nonlocal model.”
A fractional Yamabe flow and some applications (2011, background): “d [57]. We also consider the unnormalized fractional Yamabe ﬂow ∂vN ∂t = −Pσ(v) on Sn ×(0,∞), or ∂uN ∂t = −(−∆)σu in Rn ×(0,∞). The second one is a fractional porous medium equation studied, e.g., in [2, 28, 20, 29, 53], where it is taken the form ( ut = −(−∆)σ(|u|m−1u) in Rn ×(0,∞), u(·,0) = u0 in ”
Classical solutions and higher regularity for nonlinear fractional diffusion equations (2013, methodology): “1) occur in boundary heat control, as already mentioned by Athanasopoulos and Caffarelli [2] , where they refer to the model formulated in the book by Duvaut and Lions [10], and use the extension technique of Caffarelli and Silvestre.”
Infinite Speed of Propagation and Regularity of Solutions to the Fractional Porous Medium Equation in General Domains (2015, methodology): “Also, the paper of Athanasopoulos and Caffarelli relies on the so-called extension property for the fractional Laplacian and does not generalize to general operators as in (1.3).”
The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion (2017, methodology): “We have written a detailed description of this model in the survey paper [246], where we give references to the physical motivations, among them [21, 155, 154, 156], the literature, and the mathematical developments until 2013 approximately.”
On the Cauchy problem for a general fractional porous medium equation with variable density (2013, background): “1) makes perfect sense, as it can be regarded both as a generalization of problem (1.3) and as nonlocal version of problem (1.2). Moreover, problem (1.1) arises in many physical situations (see, e.g. [1], [13] , [14]) such as diﬀusions in inhomogeneous media and is particularly interesting from a pr”
On the regularity of the non-dynamic parabolic fractional obstacle problem (2016, background): “In [3] this degenerate equation has been considered in the study of the continuity of the temperature in boundary heat control problems with fractional diffusion.”
Recent progress in the theory of Nonlinear Diffusion with Fractional Laplacian Operators (2014, methodology): “The idea of the proof is as follows: thanks to the results of Athanasopoulos and Caffarelli [11], we know that bounded weak solutions are C regular for some α ∈ (0, 1).”
A General Fractional Porous Medium Equation (2011, background): “The above-mentioned regularity result of [3] applies for bounded solutions to the equation ∂β(v) ∂t + (−∆)v = 0 in some ball B ⊂ R and t > 0, with a nondegeneracy condition on the constitutive monotone function β.”
Quantitative local and global a priori estimates for fractional nonlinear diffusion equations (2012, methodology): “ ˙2@2 x( ˆ). When is a power we recover equation (1.1). Equations like the last one (in several space dimensions) occur in boundary heat control, as already mentioned by Athanasopoulos and Caarelli [3], where they refer to the model formulated in the book by Duvaut and Lions [21], and use the so-cal”