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In this chapter we will deal with the Reaction-Diffusion (RD) system \(\displaystyle \partial _t z=\mathbf {D}\Delta _x z + M(x)z + \big ( W(x)|z|^{p-2}+Q(x)|z|^{4/N} \big )\beta z \) where the diffusion coefficients \(\mathbf {D}\) is defined in ( 2.6 ) and M, W and Q are external potentials with M being one of the following form \(\displaystyle M(x)= \begin {pmatrix} -\text{Id}-V(x)&0\\ 0&\text{Id} + V(x) \end {pmatrix}\quad \text{or} \quad M(x)= \begin {pmatrix} -\text{Id}&-V(x)\\ V(x)&\text{Id} \end {pmatrix}. \)

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Effect of External Potentials in a Coupled System Reaction-Diffusion

  • 章节

  • 发表日期：

    2025年

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  • Yanheng Ding,
  • Tian Xu

摘要

In this chapter we will deal with the Reaction-Diffusion (RD) system \(\displaystyle \partial _t z=\mathbf {D}\Delta _x z + M(x)z + \big ( W(x)|z|^{p-2}+Q(x)|z|^{4/N} \big )\beta z \) where the diffusion coefficients \(\mathbf {D}\) is defined in ( 2.6 ) and M, W and Q are external potentials with M being one of the following form \(\displaystyle M(x)= \begin {pmatrix} -\text{Id}-V(x)&0\\ 0&\text{Id} + V(x) \end {pmatrix}\quad \text{or} \quad M(x)= \begin {pmatrix} -\text{Id}&-V(x)\\ V(x)&\text{Id} \end {pmatrix}. \)