On the internal transition layer to some inhomogeneous semilinear problems: Interface location

Sônego, Maicon

doi:10.1016/j.jmaa.2021.125266

Cited by 3 publications

(3 citation statements)

References 14 publications

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“…First we also assume that Q is simply connected. We borrow the idea of [30] (see also [28]) to define a sequence of functions b (z, t; τ…”

Section: Local Minimummentioning

confidence: 99%

“…First we also assume that is simply connected. We borrow the idea of [30] (see also [28]) to define a sequence of functions where is the solution of (2.2). Given satisfying and , we define by …”

Section: Local Minimummentioning

confidence: 99%

“…Recently, in one-dimensional domain case (Ω = (0, 1)), for general a(x) and f satisfying conditions (f 1 )-(f 3 ), [28] obtains the following results. Proposition 1.2.…”

Section: Introductionmentioning

confidence: 97%

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Locations of interior transition layers to inhomogeneous transition problems in higher -dimensional domains

Du¹

2022

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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We consider the following inhomogeneous problems \[ \begin{cases} \epsilon^{2}\mbox{div}(a(x)\nabla u(x))+f(x,u)=0 & \text{ in }\Omega,\\ \frac{\partial u}{\partial \nu}=0 & \text{ on }\partial \Omega,\\ \end{cases} \] where $\Omega$ is a smooth and bounded domain in general dimensional space $\mathbb {R}^{N}$ , $\epsilon >0$ is a small parameter and function $a$ is positive. We respectively obtain the locations of interior transition layers of the solutions of the above transition problems that are $L^{1}$ -local minimizer and global minimizer of the associated energy functional.

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“…First we also assume that Q is simply connected. We borrow the idea of [30] (see also [28]) to define a sequence of functions b (z, t; τ…”

Section: Local Minimummentioning

confidence: 99%