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mathematics - analysis of pdes (38) 38
mathematics (18) 18
global existence (17) 17
mathematics, applied (15) 15
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dynamics (11) 11
muskat problem (10) 10
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analysis of pdes (7) 7
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mathematical analysis (6) 6
regularity (6) 6
existence (5) 5
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[math.math-ap]mathematics [math]/analysis of pdes [math.ap] (3) 3
critical mass (3) 3
degenerate diffusion (3) 3
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mathematical & computational biology (2) 2
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05/2011
In this lecture notes we present the equations and the physics involved in the dynamic of incompressible fluids. We present the mathematical techniques needed... 
Journal Article
09/2012
We study the evolution of the interface given by two incompressible fluids with different densities in the porous strip $\RR\times[-l,l]$. This problem is... 
Mathematics - Analysis of PDEs
Journal Article
03/2013
In this paper we show global existence of Lipschitz continuous solution for the stable Muskat problem with finite depth (confined) and initial data satisfying... 
Mathematics - Analysis of PDEs
Journal Article
06/2013
In this paper we study an aggregation equation with a general nonlocal flux. We study the local well-posedness and some conditions ensuring global existence.... 
Mathematics - Analysis of PDEs
Journal Article
11/2013
In this work we study the evolution of the free boundary between two different fluids in a porous medium where the permeability is a two dimensional step... 
Mathematics - Analysis of PDEs
Journal Article
Communications in Mathematical Sciences, ISSN 1539-6746, 2014, Volume 12, Issue 3, pp. 423 - 455
We study the evolution of the interface given by two incompressible fluids with different densities in the porous strip. This problem is known as the Muskat... 
Hele-Shaw cell | Ill-posedness | Muskat problem | Maximum principle | Darcy's law | Blow-up | Well-posedness | FLUIDS | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | well-posedness | ill-posedness | HELE-SHAW | maximum principle | FLOW | blow-up | DYNAMICS
Journal Article
SIAM journal on mathematical analysis, ISSN 1095-7154, 2014, Volume 46, Issue 2, pp. 1651 - 1680
...SIAM J. MATH. ANAL. c Vol. 46, No. 2, pp. 16511680 GLOBAL EXISTENCE FOR THE CONFINED MUSKAT PROBLEM RAFAEL GRANERO-BELINCHN Abstract. In this paper we show... 
Inhomogeneus Muskat problem | Darcy's law | Well-posedness | FLUIDS | MATHEMATICS, APPLIED | well-posedness | DYNAMICS | inhomogeneus Muskat problem | HELE-SHAW | FLOW | Maximum principle | Amplitudes | Case depth | Mathematical analysis
Journal Article
Interfaces and Free Boundaries, ISSN 1463-9963, 2014, Volume 16, Issue 2, pp. 175 - 213
In this work we study the evolution of the free boundary between two different fluids in a porous medium where the permeability is a two dimensional step... 
Maximum principle | Darcy's law | Inhomogeneous muskat problem | Blow-up | Well-posedness | FLUIDS | MATHEMATICS | MATHEMATICS, APPLIED | inhomogeneous Muskat problem | GLOBAL EXISTENCE | well-posedness | blow-up | DYNAMICS | HELE-SHAW | maximum principle | FLOW
Journal Article
Nonlinearity, ISSN 1361-6544, 2014, Volume 27, Issue 6, pp. 1471 - 1498
We exhibit a family of graphs that develop turning singularities (i.e. their Lipschitz seminorm blows up and they cease to be a graph, passing from the stable... 
Darcys law | inhomogeneous Muskat problem | turning | blow-up | computerassisted | water waves | singularity | FLUIDS | MATHEMATICS, APPLIED | DIFFERENT DENSITIES | GLOBAL EXISTENCE | WELL-POSEDNESS | HELE-SHAW | PHYSICS, MATHEMATICAL | FLOW | WATER-WAVES | DYNAMICS | Darcy's law | Infinity | Singularities | Mathematical analysis | Proving | Turning | Graphs | Boundary conditions | Permeability | Mathematics - Analysis of PDEs
Journal Article
08/2014
In this paper, we study transport equations with nonlocal velocity fields with rough initial data. We address the global existence of weak solutions of an one... 
Mathematics - Analysis of PDEs
Journal Article
09/2014
Topol. Methods Nonlinear Anal. 47 (2016), 369-387 A semilinear version of parabolic-elliptic Keller-Segel system with the \emph{critical} nonlocal diffusion is... 
Mathematics - Analysis of PDEs
Journal Article
Nonlinear analysis, ISSN 0362-546X, 2014, Volume 108, pp. 260 - 274
Journal Article
12/2014
We study the dynamics of the interface between two incompressible fluids in a two-dimensional porous medium whose flow is modeled by the Muskat equations. For... 
Mathematics - Analysis of PDEs
Journal Article
Advances in mathematics (New York. 1965), ISSN 0001-8708, 2015, Volume 269, pp. 197 - 219
In this paper, we study transport equations with nonlocal velocity fields with rough initial data. We address the global existence of weak solutions of a one... 
Transport equation | Nonlocal velocity field | Entropy | Weak solution | SINGULARITIES | Non local velocity field | ONE-DIMENSIONAL MODEL | WELL-POSEDNESS | MATHEMATICS | FRONTS | QUASI-GEOSTROPHIC EQUATIONS | MUSKAT PROBLEM | REGULARITY | DIFFUSION | BLOW-UP | BREAKDOWN
Journal Article
Nonlinearity, ISSN 0951-7715, 02/2015, Volume 28, Issue 2, pp. 435 - 461
In this paper we study a model of an interface between two fluids in a porous medium. For this model we prove several local and global well-posedness results... 
one-dimensional model | Muskat problem | porous medium | MATHEMATICS, APPLIED | MAXIMUM PRINCIPLE | GLOBAL EXISTENCE | DYNAMICS | WELL-POSEDNESS | HELE-SHAW | MODEL | PHYSICS, MATHEMATICAL | Porous media | Fluids | Computational fluid dynamics | Fluid flow | Nonlinearity | Mathematical models | Boundaries | Mathematics - Analysis of PDEs
Journal Article
Nonlinearity, ISSN 0951-7715, 04/2015, Volume 28, Issue 4, pp. 1103 - 1133
We study a nonlocal equation, analogous to the Kuramoto-Sivashinsky equation, in which short waves are stabilized by a possibly fractional diffusion of order... 
Kuramoto-Sivashinsky equation | spatial chaos | attractor | MATHEMATICS, APPLIED | MAXIMUM PRINCIPLE | STABILITY | PHYSICS, MATHEMATICAL | ANALYTICITY | WAVES | MUSKAT PROBLEM | REGULARITY | BOUNDS | PROPAGATION | Chaos theory | Mathematical analysis | Uniqueness | Traveling waves | Nonlinearity | Mathematical models | Diffusion | Short wave | Mathematics - Analysis of PDEs
Journal Article
04/2015
Nonlinearity 29 (2016) 3810-3836 We show that solutions to the parabolic-elliptic Keller-Segel system on ${\mathbb S}^1$ with critical fractional diffusion... 
Mathematics - Analysis of PDEs
Journal Article
Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 01/2016, Volume 26, Issue 1, pp. 111 - 160
Journal Article
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