Results 21 to 30 of about 658 (73)
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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Advanced Nonlinear Studies, 2021 In this article, we are interested in multi-bump solutions of the singularly perturbed ...
Jin Sangdon
doaj +1 more source
A survey of partial differential equations with piecewise continuous arguments
International Journal of Mathematics and Mathematical Sciences, Volume 18, Issue 2, Page 209-228, 1995., 1995 Some work is described and new topics are posed on initial and boundary‐value problems for partial differential equations whose arguments have intervals of constancy. These equations are of considerable theoretical and applied interest.
Joseph Wiener, Lokenath Debnath
wiley +1 more source
Analysis of a diffuse interface model of multispecies tumor growth [PDF]
, 2015 We consider a diffuse interface model for tumor growth recently proposed in [Y. Chen, S.M. Wise, V.B. Shenoy, J.S. Lowengrub, A stable scheme for a nonlinear, multiphase tumor growth model with an elastic membrane, Int. J. Numer. Methods Biomed. Eng., 30
Dai, Mimi +4 more
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Open Mathematics, 2018 The main purpose of this paper is to study the initial layer problem and the infinite Prandtl number limit of Rayleigh-Bénard convection with an ill prepared initial data.
Fan Xiaoting +3 more
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A parabolic differential equation with unbounded piecewise constant delay
International Journal of Mathematics and Mathematical Sciences, Volume 15, Issue 2, Page 339-346, 1992., 1991 A partial differential equation with the argument [λt] is studied, where [•] denotes the greatest integer function. The infinite delay t − [λt] leads to difference equations of unbounded order.
Joseph Wiener, Lokenath Debnath
wiley +1 more source
Semiclassical stationary states for nonlinear Schr\"odinger equations under a strong external magnetic field [PDF]
, 2015 We construct solutions to the nonlinear magnetic Schr\"odinger equation $$ \left\{ \begin{aligned} - \varepsilon^2 \Delta_{A/\varepsilon^2} u + V u &= \lvert u\rvert^{p-2} u & &\text{in}\ \Omega,\\ u &= 0 & &\text{on}\ \partial\Omega, \end{aligned}
Di Cosmo, Jonathan +1 more
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A survey on some vanishing viscosity limit results
Advances in Nonlinear Analysis, 2023 We present a survey concerning the convergence, as the viscosity goes to zero, of the solutions to the three-dimensional evolutionary Navier-Stokes equations to solutions of the Euler equations.
Beirão da Veiga Hugo, Crispo Francesca
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Boundary value problems for partial differential equations with piecewise contant delay
International Journal of Mathematics and Mathematical Sciences, Volume 14, Issue 2, Page 363-379, 1991., 1991 The influence of certain discontinuous delays on the behavior of solutions to some typical equations of mathematical physics is studied.
Joseph Wiener
wiley +1 more source
Variational problems with singular perturbation [PDF]
, 2005 In this paper, we construct the local minimum of a certain variational problem which we take in the form $\mathrm{inf}\int_\Omega\left\{\frac{\epsilon}{2}kg^2|\nabla w|^2+\frac{1}{4\epsilon}f^2g^4(1-w^2)^2\right\}\,\mathrm{d}x$, where $\epsilon$ is a ...
Norbury, John, Yeh, Li-Chin
core +2 more sources