Results 1 to 10 of about 79 (79)
On the transport limit of singularly perturbed convection–diffusion problems on networks
Mathematical Methods in the Applied Sciences, Volume 44, Issue 6, Page 5005-5020, April 2021., 2021 We consider singularly perturbed convection–diffusion equations on one‐dimensional networks (metric graphs) as well as the transport problems arising in the vanishing diffusion limit. Suitable coupling conditions at inner vertices are derived that guarantee conservation of mass and dissipation of a mathematical energy which allows us to prove stability
Herbert Egger, Nora Philippi
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Advanced Nonlinear Studies, 2022 This article studies point concentration phenomena of nonlinear Schrödinger equations with magnetic potentials and constant electric potentials. The existing results show that a common magnetic field has no effect on the locations of point concentrations,
Wang Liping, Zhao Chunyi
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Advances in Nonlinear Analysis, 2023 We establish fine bounds for best constants of the fractional subcritical Sobolev embeddings W0s,p(Ω)↪Lq(Ω),{W}_{0}^{s,p}(\Omega )\hspace{0.33em}\hookrightarrow \hspace{0.33em}{L}^{q}(\Omega ), where N≥1N\ge 1 ...
Cassani Daniele, Du Lele
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Advanced Nonlinear Studies, 2023 In this work, we analyze the asymptotic behavior of a class of quasilinear elliptic equations defined in oscillating (N+1)\left(N+1)-dimensional thin domains (i.e., a family of bounded open sets from RN+1{{\mathbb{R}}}^{N+1}, with corrugated bounder ...
Nakasato Jean Carlos +1 more
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On the singularly perturbation fractional Kirchhoff equations: Critical case
Advances in Nonlinear Analysis, 2022 This article deals with the following fractional Kirchhoff problem with critical exponent a+b∫RN∣(−Δ)s2u∣2dx(−Δ)su=(1+εK(x))u2s∗−1,inRN,\left(a+b\mathop{\int }\limits_{{{\mathbb{R}}}^{N}}| {\left(-\Delta )}^{\tfrac{s}{2}}u\hspace{-0.25em}{| }^{2}{\rm{d ...
Gu Guangze, Yang Zhipeng
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Inviscid, zero Froude number limit of the viscous shallow water system
Open Mathematics, 2021 In this paper, we study the inviscid and zero Froude number limits of the viscous shallow water system. We prove that the limit system is represented by the incompressible Euler equations on the whole space.
Yang Jianwei, Liu Mengyu, Hao Huiyun
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Continuum limits of particles interacting via diffusion
Abstract and Applied Analysis, Volume 2004, Issue 3, Page 215-237, 2004., 2004 We consider a two‐phase system mainly in three dimensions and we examine the coarsening of the spatial distribution, driven by the reduction of interface energy and limited by diffusion as described by the quasistatic Stefan free boundary problem. Under the appropriate scaling we pass rigorously to the limit by taking into account the motion of the ...
Nicholas D. Alikakos +2 more
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Fractional parabolic problems with a nonlocal initial condition
Moroccan Journal of Pure and Applied Analysis, 2017 In this work we will consider a class of non local parabolic problems with nonlocal initial condition, more precisely we deal with the ...
Abdellaoui B. +2 more
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Asymptotic solutions of diffusion models for risk reserves
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 35, Page 2221-2239, 2003., 2003 We study a family of diffusion models for risk reserves which account for the investment income earned and for the inflation experienced on claim amounts. After we defined the process of the conditional probability of ruin over finite time and imposed the appropriate boundary conditions, classical results from the theory of diffusion processes turn the
S. Shao
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Oscillatory and periodic solutions to a diffusion equation of neutral type
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 2, Page 313-348, 1999., 1999 We examine a PDE with piecewise constant time delay. The equation is of neutral type since it contains the derivative ut at different values of the t‐argument. Furthermore, the argument deviation changes its sign within intervals of unit length, so that the given PDE is alternately of retarded and advanced type.
Joseph Wiener, William Heller
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