Results 21 to 30 of about 1,990 (139)
A free boundary problem describing the saturated‐unsaturated flow in a porous medium
Abstract and Applied Analysis, Volume 2004, Issue 9, Page 729-755, 2004., 2004 This paper presents a functional approach to a nonlinear model describing the complete physical process of water infiltration into an unsaturated soil, including the saturation occurrence and the advance of the wetting front. The model introduced in this paper involves a multivalued operator covering the simultaneous saturated and unsaturated flow ...
Gabriela Marinoschi
wiley +1 more source
Extinction properties of solutions for a fast diffusion equation with nonlocal source
Boundary Value Problems, 2013 In this paper, we investigate extinction properties of nonnegative nontrivial solutions for an initial boundary value problem of a fast diffusion equation with a nonlocal source in bounded domain.
Z. Fang, Mei Wang
semanticscholar +2 more sources
On distributional solutions of local and nonlocal problems of porous medium type [PDF]
, 2017 We present a theory of well-posedness and a priori estimates for bounded distributional (or very weak) solutions of $$\partial_tu-\mathfrak{L}^{\sigma,\mu}[\varphi(u)]=g(x,t)\quad\quad\text{in}\quad\quad \mathbb{R}^N\times(0,T),$$ where $\varphi$ is ...
del Teso, Félix +2 more
core +3 more sources
Intrinsic Harnack estimates for some doubly nonlinear degenerate parabolic equations
Advances in Differential Equations, 2008 We prove an intrinsic Harnack inequality for non-negative local weak solutions of a wide class of doubly nonlinear degenerate parabolic equations whose prototype is ut − div(u|Du|Du) = 0, p > 2, m > 1.
S. Fornaro, M. Sosio
semanticscholar +1 more source
On a nonlinear compactness lemma in Lp(0, T; B)
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 27, Page 1725-1730, 2003., 2003 We consider a nonlinear counterpart of a compactness lemma of Simon (1987), which arises naturally in the study of doubly nonlinear equations of elliptic‐parabolic type. This paper was motivated by previous results of Simon (1987), recently sharpened by Amann (2000), in the linear setting, and by a nonlinear compactness argument of Alt and Luckhaus ...
Emmanuel Maitre
wiley +1 more source
Time-periodic solutions for a driven sixth-order Cahn-Hilliard type equation
Boundary Value Problems, 2013 We study a driven sixth-order Cahn-Hilliard type equation which arises naturally as a continuum model for the formation of quantum dots and their faceting. Based on the Leray-Schauder fixed point theorem, we prove the existence of time-periodic solutions.
Changchun Liu, Aibo Liu, Hui Tang
semanticscholar +2 more sources
From Nash to Cournot-Nash equilibria via the Monge-Kantorovich problem [PDF]
, 2014 The notion of Nash equilibria plays a key role in the analysis of strategic interactions in the framework of $N$ player games. Analysis of Nash equilibria is however a complex issue when the number of players is large.
Blanchet, Adrien, Carlier, Guillaume
core +6 more sources
Null controllability of degenerate parabolic cascade systems
, 2011 . In this paper, we study the null controllability of degenerate semilinear cas-cade parabolic systems with one control force. The key tool is the Carleman estimatesdeveloped recently for degenerate one dimension parabolic equations.
E. Hassi +3 more
semanticscholar +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 53, Page 3385-3411, 2003., 2003 We study the hp version of three families of Eulerian‐Lagrangian mixed discontinuous finite element (MDFE) methods for the numerical solution of advection‐diffusion problems. These methods are based on a space‐time mixed formulation of the advection‐diffusion problems.
Hongsen Chen, Zhangxin Chen, Baoyan Li
wiley +1 more source
The nonlinear diffusion equation of the ideal barotropic gas through a porous medium
Open Mathematics, 2017 The nonlinear diffusion equation of the ideal barotropic gas through a porous medium is considered. If the diffusion coefficient is degenerate on the boundary, then the solutions may be controlled by the initial value completely, the well-posedness of ...
Zhan Huashui
doaj +1 more source