The Location and Stability of Interface Solutions of an Inhomogeneous Parabolic Problem
SIAM Journal on Applied Mathematics, 2001 This paper is concerned with interface solutions of a reaction-diffusion problem with a small diffusion coefficient. After a change of timescale, the problem is \[ \varepsilon^2 w_\tau= \varepsilon^2 w_{xx}+ f^2(x) (g^2(x)- w^2)w;\;w(x,0)= \Phi(x),\;x\in (0,1)\tag{1} \] with the Neumann boundary condition; \(f\) and \(g\) are smooth strictly positive ...
Norbury, J, Yeh, L
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Multiblock Mortar Mixed Approach for Second Order Parabolic Problems
Mathematics, 2019 In this paper, the multiblock mortar mixed approximation of second order parabolic partial differential equations is considered. In this method, the simulation domain is decomposed into the non-overlapping subdomains (blocks), and a physically-meaningful
Muhammad Arshad +2 more
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Theory of an Automatic Seepage Meter and Ramifications for Applications
Water Resources Research, 2023 A new approach for measuring fluxes across surface water—groundwater interfaces was recently proposed. The Automatic Seepage Meter (ASM) is equipped with a precise water level sensor and digital memory that analyzes water level time series in a vertical ...
Vitaly A. Zlotnik +6 more
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Pushing of Interstitial Elements in the Transition Zone under the Growing Diffusion Layers
Фізика і хімія твердого тіла, 2016 The kinetics of diffusion of interstitial elements on the example of diffusion saturation with boron and silicon iron- carbon matrix ( - iron) was considered .
A. I. Nesterenko, N. G. Nesterenko
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High-order numerical methods for 2D parabolic problems in single and composite domains [PDF]
, 2017 In this work, we discuss and compare three methods for the numerical approximation of constant- and variable-coefficient diffusion equations in both single and composite domains with possible discontinuity in the solution/flux at interfaces, considering (
Epshteyn, Yekaterina +6 more
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Detecting Interfaces in a Parabolic‐Elliptic Problem from Surface Measurements
SIAM Journal on Numerical Analysis, 2007 Assuming that the heat capacity of a body is negligible outside certain inclusions the heat equation degenerates to a parabolic-elliptic interface problem. In this work we aim to detect these interfaces from thermal measurements on the surface of the body. We deduce an equivalent variational formulation for the parabolic-elliptic problem and give a new
Florian Frühauf +2 more
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Generation of interface for an Allen-Cahn equation with nonlinear diffusion [PDF]
, 2009 In this note, we consider a nonlinear diffusion equation with a bistable reaction term arising in population dynamics. Given a rather general initial data, we investigate its behavior for small times as the reaction coefficient tends to infinity: we ...
Alfaro +12 more
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Studying behavior of the asymptotic solutions to P-Laplacian type diffusion-convection model [PDF]
مجلة جامعة الانبار للعلوم الصرفةThe rescaling method is presented to allow us to establish nonnegative local solutions to the evolution of the Cauchy problem (CP) of the nonlinear degenerate parabolic p-Laplacian process with conservation laws that are posed in one-dimensional space ...
Habeeb Aal-Rkhais, Ruba Qasim
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A Priori Error Bounds for Parabolic Interface Problems with Measure Data
Numerical Analysis and Applications, 2023 This article studies a priori error analysis for linear parabolic interface problems with measure data in time in a bounded convex polygonal domain in $\mathbb{R}^2$. We have used the standard continuous fitted finite element discretization for the space.
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Non-uniqueness results for entropy two-phase solutions of forward-backward parabolic problems with unstable phase [PDF]
, 2013 This paper study the well--posedness of the entropy formulation given by Plotnikov in [{Differential Equations}, 30 (1994), pp. 614--622] for forward-backward parabolic problem obtained as singular limit of a proper pseudoparabolic approximation.
Terracina, Andrea
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