Results 71 to 80 of about 12,475 (200)
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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Existence and uniqueness for a coupled parabolic‐hyperbolic model of MEMS
Mathematical Methods in the Applied Sciences, Volume 47, Issue 7, Page 6310-6353, 15 May 2024.Local wellposedness for a nonlinear parabolic‐hyperbolic coupled system modeling Micro‐Electro‐Mechanical System (MEMS) is studied. The particular device considered is a simple capacitor with two closely separated plates, one of which has motion modeled by a semilinear hyperbolic equation.
Heiko Gimperlein +2 more
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Expanding solutions of quasilinear parabolic equations
Communications on Pure and Applied Analysis, 2021 By using the theory of maximal $L^{q}$-regularity and methods of singular analysis, we show a Taylor's type expansion--with respect to the geodesic distance around an arbitrary point--for solutions of quasilinear parabolic equations on closed manifolds. The powers of the expansion are determined explicitly by the local geometry, whose reflection to the
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A duality for prescribed mean curvature graphs in Riemannian and Lorentzian Killing submersions
Mathematische Nachrichten, Volume 297, Issue 5, Page 1581-1600, May 2024.Abstract We develop a conformal duality for space‐like graphs in Riemannian and Lorentzian three‐manifolds that admit a Riemannian submersion over a Riemannian surface whose fibers are the integral curves of a Killing vector field, which is time‐like in the Lorentzian case.
Andrea Del Prete +2 more
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Electronic Journal of Differential Equations, 2002 We present existence and stability results for periodic solutions of quasilinear parabolic equation related to Leray-Lions's type operators. To prove existence and localization, we use the penalty method; while for stability we use an approximation ...
Abderrahmane El Hachimi +1 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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Potential estimates and quasilinear parabolic equations with measure data [PDF]
, 2014 In this paper, we study the existence and regularity of the quasilinear parabolic equations: $$u_t-\text{div}(A(x,t,\nabla u))=B(u,\nabla u)+\mu$$ in $\mathbb{R}^{N+1}$, $\mathbb{R}^N\times(0,\infty)$ and a bounded domain $\Omega\times (0,T)\subset ...
Quoc-hung Nguyen, See Profile
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The Mullins–Sekerka problem via the method of potentials
Mathematische Nachrichten, Volume 297, Issue 5, Page 1960-1977, May 2024.Abstract It is shown that the two‐dimensional Mullins–Sekerka problem is well‐posed in all subcritical Sobolev spaces Hr(R)$H^r({\mathbb {R}})$ with r∈(3/2,2)$r\in (3/2,2)$. This is the first result, where this issue is established in an unbounded geometry.
Joachim Escher +2 more
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Directed mean curvature flow in noisy environment
Communications on Pure and Applied Mathematics, Volume 77, Issue 3, Page 1850-1939, March 2024.Abstract We consider the directed mean curvature flow on the plane in a weak Gaussian random environment. We prove that, when started from a sufficiently flat initial condition, a rescaled and recentred solution converges to the Cole–Hopf solution of the KPZ equation.
Andris Gerasimovičs +2 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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