Results 1 to 10 of about 1,088 (84)
On the relativistic heat equation in one space dimension
Proceedings of the London Mathematical Society, Volume 107, Issue 6, Page 1395-1423, December 2013., 2013 We study the relativistic heat equation in one space dimension. We prove a local regularity result when the initial datum is locally Lipschitz in its support. We propose a numerical scheme that captures the known features of the solutions and allows for analysing further properties of their qualitative behaviour.
J. A. Carrillo, V. Caselles, S. Moll
wiley +1 more source
Advanced Nonlinear Studies, 2022 The chemotaxis–Stokes system nt+u⋅∇n=∇⋅(D(n)∇n)−∇⋅(nS(x,n,c)⋅∇c),ct+u⋅∇c=Δc−nc,ut=Δu+∇P+n∇Φ,∇⋅u=0,\left\{\begin{array}{l}{n}_{t}+u\cdot \nabla n=\nabla \cdot (D\left(n)\nabla n)-\nabla \cdot (nS\left(x,n,c)\cdot \nabla c),\\ {c}_{t}+u\cdot \nabla c ...
Winkler Michael
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Modeling and Simulation of a Bacterial Biofilm That Is Controlled by pH and Protonated Lactic Acids
Computational and Mathematical Methods in Medicine, Volume 9, Issue 1, Page 47-67, 2008., 2008 We present a mathematical model for growth and control of facultative anaerobic bacterial biofilms in nutrient rich environments. The growth of the microbial population is limited by protonated lactic acids and the local pH value, which in return are altered as the microbial population changes.
Hassan Khassehkhan, Hermann J. Eberl
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Theoretical and numerical analysis of a degenerate nonlinear cubic Schrödinger equation
Moroccan Journal of Pure and Applied Analysis, 2022 In this paper, we are interested in some theoretical and numerical studies of a special case of a degenerate nonlinear Schrödinger equation namely the so-called Gross-Pitaevskii Equation(GPE).
Alahyane Mohamed +2 more
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A nonlinear parabolic problem with singular terms and nonregular data [PDF]
, 2019 We study existence of nonnegative solutions to a nonlinear parabolic boundary value problem with a general singular lower order term and a nonnegative measure as nonhomogeneous datum, of the form $$ \begin{cases} \dys u_t - \Delta_p u = h(u)f ...
Oliva, Francescantonio +1 more
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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
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A cross-diffusion system derived from a Fokker-Planck equation with partial averaging [PDF]
, 2016 A cross-diffusion system for two compoments with a Laplacian structure is analyzed on the multi-dimensional torus. This system, which was recently suggested by P.-L.
Jüngel, Ansgar, Zamponi, Nicola
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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
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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
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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
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