Results 51 to 60 of about 658 (73)
Regularity for critical fractional Choquard equation with singular potential and its applications
Advances in Nonlinear AnalysisWe study the following fractional Choquard equation (−Δ)su+u∣x∣θ=(Iα*F(u))f(u),x∈RN,{\left(-\Delta )}^{s}u+\frac{u}{{| x| }^{\theta }}=({I}_{\alpha }* F\left(u))f\left(u),\hspace{1em}x\in {{\mathbb{R}}}^{N}, where N⩾3N\geqslant 3, s∈12,1s\in \left ...
Liu Senli, Yang Jie, Su Yu
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Two methods for replacing Dirichlet\u27s boundary condition by Robin\u27s boundary condition via penalization [PDF]
, 1999 In this paper we present two methods for replacing Dirichlet\u27s problem by a sequence of Robin\u27s problems. We study the linear parabolic equation as a model problem. We use the first method for the problem with irregular boundary data and the second
E. Marušić-Paloka
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Persistence of a unique periodic wave train in convecting shallow water fluid
Demonstratio MathematicaThe coexistence of a traveling pulse and a periodic traveling wave was established in a convecting shallow water model when taking a nonlinear buoyancy term uuxu{u}_{x}.
Yang Sumin, Wen Qian
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Uniform convergence of adversarially robust classifiers
European Journal of Applied MathematicsIn recent years, there has been significant interest in the effect of different types of adversarial perturbations in data classification problems. Many of these models incorporate the adversarial power, which is an important parameter with an associated
Rachel Morris, Ryan Murray
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Demonstratio MathematicaThis study is devoted to designing two hybrid computational algorithms to find approximate solutions for a class of singularly perturbed parabolic convection–diffusion–reaction problems with two small parameters.
Ansari Khursheed J. +2 more
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A singular perturbation result for a class of periodic-parabolic BVPs
Open MathematicsIn this article, we obtain a very sharp version of some singular perturbation results going back to Dancer and Hess [Behaviour of a semilinear periodic-parabolic problem when a parameter is small, Lecture Notes in Mathematics, Vol. 1450, Springer-Verlag,
Cano-Casanova Santiago +2 more
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European Journal of Applied MathematicsThe Cahn–Hilliard model with reaction terms can lead to situations in which no coarsening is taking place and, in contrast, growth and division of droplets occur which all do not grow larger than a certain size.
Harald Garcke +3 more
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Existence and uniqueness of solution for a singular elliptic differential equation
Advances in Nonlinear AnalysisIn this article, we are concerned about the existence, uniqueness, and nonexistence of the positive solution for: −Δu−12(x⋅∇u)=μh(x)uq−1+λu−up,x∈RN,u(x)→0,as∣x∣→+∞,\left\{\begin{array}{l}-\Delta u-\frac{1}{2}\left(x\cdot \nabla u)=\mu h\left(x){u}^{q-1}+\
Gu Shanshan, Yang Bianxia, Shao Wenrui
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European Journal of Applied MathematicsIn the second part of this series of papers, we address the same evolution problem that was considered in part 1 (see [16]), namely the nonlocal Fisher-KPP equation in one spatial dimension, \begin{equation*} u_t = D u_{xx} + u(1-\phi *u), \end ...
David J. Needham, John Billingham
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European Journal of Applied MathematicsWe study the Cauchy problem on the real line for the nonlocal Fisher-KPP equation in one spatial dimension, \begin{equation*} u_t = D u_{xx} + u(1-\phi *u), \end{equation*} where $\phi *u$ is a spatial convolution with the top hat kernel,
David John Needham +3 more
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