The higher integrability of weak solutions of porous medium systems
Advances in Nonlinear Analysis, 2018 In this paper we establish that the gradient of weak solutions to porous medium-type systems admits the self-improving property of higher integrability.
Bögelein Verena +3 more
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A constructive method for convex solutions of a class of nonlinear Black-Scholes equations
Advances in Nonlinear Analysis, 2019 In this work, we are concerned with the theoretical study of a nonlinear Black-Scholes equation resulting from market frictions. We will focus our attention on Barles and Soner’s model where the volatility is enlarged due to the presence of transaction ...
Abounouh Mostafa +3 more
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Near Field Asymptotic Behavior for the Porous Medium Equation on the Half-Line
Advanced Nonlinear Studies, 2017 Kamin and Vázquez [11] proved in 1991 that solutions to the Cauchy–Dirichlet problem for the porous medium equation ut=(um)xx${u_{t}=(u^{m})_{xx}}$, m>1${m>1}$, on the half-line with zero boundary data and nonnegative compactly supported integrable ...
Cortázar Carmen +2 more
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Semi-wavefront solutions in models of collective movements with density-dependent diffusivity [PDF]
arXiv, 2017 This paper deals with a nonhomogeneous scalar parabolic equation with possibly degenerate diffusion term; the process has only one stationary state. The equation can be interpreted as modeling collective movements (crowd dynamics, for instance).
arxiv
On the Cauchy problem of a degenerate parabolic-hyperbolic PDE with Lévy noise
Advances in Nonlinear Analysis, 2017 In this article, we deal with the stochastic perturbation of degenerate parabolic partial differential equations (PDEs). The particular emphasis is on analyzing the effects of a multiplicative Lévy noise on such problems and on establishing a well ...
Biswas Imran H. +2 more
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Very singular solutions for the thin film equation with absorption [PDF]
arXiv, 2009 Self-similar large time behaviour of weak solutions of the fourth-order parabolic thin film equations with absorption is studued.
arxiv
System of degenerate parabolic p-Laplacian
Open MathematicsIn this article, we study the mathematical properties of the solution u=(u1,…,uk){\bf{u}}=({u}^{1},\ldots ,{u}^{k}) to the degenerate parabolic system ut=∇⋅(∣∇u∣p−2∇u),(p>2).{{\bf{u}}}_{t}=\nabla \hspace{0.25em}\cdot \hspace{0.25em}({| \nabla {\bf{u}}| }^
Kim Sunghoon, Lee Ki-Ahm
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An algorithm for one-dimensional Generalized Porous Medium Equations: interface tracking and the hole filling problem [PDF]
arXiv, 2014 Based on results of E. DiBenedetto and D. Hoff we propose an explicit finite difference scheme for the one dimensional Generalized Porous Medium Equation $\partial_t u=\partial_{xx}^2 \Phi(u)$. The scheme allows to track the moving free boundaries and captures the hole filling phenomenon when two free boundaries collide. We give an abstract convergence
arxiv
Regularity for solutions of the two-phase Stefan problem [PDF]
arXiv, 2005 We consider local solutions of the two-phase Stefan problem with a "mushy" region. We show that if a (distributional) solution u is locally square integrable then the temperature is continuous.
arxiv
On a class of fully nonlinear parabolic equations
Advances in Nonlinear Analysis, 2016 We study the homogeneous Dirichlet problem for the fully nonlinear ...
Antontsev Stanislav, Shmarev Sergey
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