Results 41 to 50 of about 1,062 (82)

System of degenerate parabolic p-Laplacian

Open Mathematics
In 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
doaj   +1 more source

Pointwise Gradient Estimates in Multi-dimensional Slow Diffusion Equations with a Singular Quenching Term

Advanced Nonlinear Studies, 2020
We consider the high-dimensional equation ∂t⁡u-Δ⁢um+u-β⁢χ{u>0}=0{\partial_{t}u-\Delta u^{m}+u^{-\beta}{\chi_{\{u>0\}}}=0}, extending the mathematical treatment made in 1992 by B. Kawohl and R. Kersner for the one-dimensional case.
Dao Nguyen Anh, Díaz Jesus Ildefonso, Nguyen Quan Ba Hong   +2 more
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Wiener-Landis criterion for Kolmogorov-type operators

, 2017
We establish a necessary and sufficient condition for a boundary point to be regular for the Dirichlet problem related to a class of Kolmogorov-type equations. Our criterion is inspired by two classical criteria for the heat equation: the Evans-Gariepy's
Kogoj, A. E., Lanconelli, E., Tralli, G.
core   +1 more source

Hölder gradient estimates for a class of singular or degenerate parabolic equations

Advances in Nonlinear Analysis, 2017
We prove interior Hölder estimates for the spatial gradients of the viscosity solutions to the singular or degenerate parabolic ...
Imbert Cyril, Jin Tianling, Silvestre Luis   +2 more
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On the Two-phase Fractional Stefan Problem

Advanced Nonlinear Studies, 2020
The classical Stefan problem is one of the most studied free boundary problems of evolution type. Recently, there has been interest in treating the corresponding free boundary problem with nonlocal diffusion.
del Teso Félix, Endal Jørgen, Vázquez Juan Luis   +2 more
doaj   +1 more source

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, Duzaar Frank, Korte Riikka, Scheven Christoph   +3 more
doaj   +1 more source

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, Al Moatassime Hassan, Driouch Aicha, Goubet Olivier   +3 more
doaj   +1 more source

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., Majee Ananta K., Vallet Guy   +2 more
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Gradient flow approach to an exponential thin film equation: global existence and latent singularity

, 2018
In this work, we study a fourth order exponential equation, $u_t=\Delta e^{-\Delta u},$ derived from thin film growth on crystal surface in multiple space dimensions.
Gao, Yuan, Liu, Jian-Guo, Lu, Xin Yang
core   +1 more source

Global existence and blow-up of solutions to pseudo-parabolic equation for Baouendi-Grushin operator

Open Mathematics
In this note, we study a global existence and blow-up of the positive solutions to the initial-boundary value problem of the nonlinear pseudo-parabolic equation for the Baouendi-Grushin operator.
Dukenbayeva Aishabibi
doaj   +1 more source