Results 61 to 70 of about 1,364,487 (206)
Mathematical Methods in the Applied Sciences, Volume 48, Issue 16, Page 14890-14908, 15 November 2025.ABSTRACT We analyze nonlinear degenerate coupled partial differential equation (PDE)‐PDE and PDE‐ordinary differential equation (ODE) systems that arise, for example, in the modelling of biofilm growth. One of the equations, describing the evolution of a biomass density, exhibits degenerate and singular diffusion.
K. Mitra, S. Sonner
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Electronic Journal of Differential Equations, 2013 In this article, we study a class of nonlocal quasilinear parabolic variational inequality involving $p(x)$-Laplacian operator and gradient constraint on a bounded domain.
Mingqi Xiang, Yongqiang Fu
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Известия высших учебных заведений: Нефть и газ, 2018 The article deals with the classical mathematical model of filtration of two immiscible liquids in a non-deformable porous medium taking into account capillary forces. It is the Muskat - Leverett model. The model is based on the experimentally determined
I. G. Telegin, O. B. Bocharov
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Muskat–Leverett Two‐Phase Flow in Thin Cylindric Porous Media: Asymptotic Approach
Studies in Applied Mathematics, Volume 155, Issue 5, November 2025.ABSTRACT A reduced‐dimensional asymptotic modeling approach is presented for the analysis of two‐phase flow in a thin cylinder with an aperture of order O(ε)$\mathcal {O}(\varepsilon)$, where ε$\varepsilon$ is a small positive parameter. We consider a nonlinear Muskat–Leverett two‐phase flow model expressed in terms of a fractional flow formulation and
Taras Mel'nyk, Christian Rohde
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Studies in Applied Mathematics, Volume 155, Issue 3, September 2025.ABSTRACT We consider reaction–diffusion systems with multiplicative noise on a spatial domain of dimension two or higher. The noise process is white in time, colored in space, and invariant under translations. Inspired by previous works on the real line, we establish the multidimensional stability of planar waves on a cylindrical domain on timescales ...
M. van den Bosch, H. J. Hupkes
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Fourier method for a quasilinear parabolic equation with periodic boundary condition [PDF]
, 2008 A multidimensional mixed problem with Neuman type periodic boundary condition is studied for the quasilinear parabolic equation ?u/?t-a2 ?2u/?x2 = f(t, x, u).
Halilov, Hüseyin, Çiftçi, İrem
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Existence of a local strong solution to the beam–polymeric fluid interaction system
Mathematische Nachrichten, Volume 298, Issue 7, Page 2327-2379, July 2025.Abstract We construct a unique local strong solution to the finitely extensible nonlinear elastic (FENE) dumbbell model of Warner‐type for an incompressible polymer fluid (described by the Navier–Stokes–Fokker–Planck equations) interacting with a flexible elastic shell.
Dominic Breit, Prince Romeo Mensah
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Homotopy regularization for a high-order parabolic equation [PDF]
, 2020 In this work, we study the solvability of the Cauchy problem for a quasilinear degenerate high-order parabolic equation...This paper has been partially supported by the Ministry of Economy and Competitiveness of Spain under research project MTM2016-80618-
Ortega García, Alejandro +1 more
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Blow-Up Analysis for a Quasilinear Degenerate Parabolic Equation with Strongly Nonlinear Source
Abstract and Applied Analysis, 2012 We investigate the blow-up properties of the positive solution of the Cauchy problem for a quasilinear degenerate parabolic equation with strongly nonlinear source ut=div(|∇um|p−2∇ul)+uq, (x,t)∈RN×(0,T), where N≥1, p>2 , and m, l, q>1, and give a ...
Pan Zheng +4 more
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Higher integrability for obstacle problem related to the singular porous medium equation
Boundary Value Problems, 2020 In this paper we study the self-improving property of the obstacle problem related to the singular porous medium equation by using the method developed by Gianazza and Schwarzacher (J. Funct. Anal. 277(12):1–57, 2019).
Qifan Li
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