On a diffusion model with absorption and production

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• 作者：Matteo Franca ; ^{franca@dipmat.univpm.it" class="auth_mail" title="E-mail the corresponding author} ; Andrea Sfecci
• 关键词：Supercritical equations ; Hardy potentials ; Radial solution ; Regular/singular ground states ; Fowler transformation ; Invariant manifold
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：34
• 期：Complete
• 页码：41-60
• 全文大小：1668 K

文摘

We discuss the structure of radial solutions of some superlinear elliptic equations which model diffusion phenomena when both absorption and production are present. We focus our attention on solutions defined in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1468121816300669&_mathId=si48.gif&_user=111111111&_pii=S1468121816300669&_rdoc=1&_issn=14681218&md5=ec03b2efabb7b3e9f58d6bf1c5013840" title="Click to view the MathML source">Rclass="mathContainer hidden">class="mathCode">$\mathbb{R}$ (regular) or in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1468121816300669&_mathId=si49.gif&_user=111111111&_pii=S1468121816300669&_rdoc=1&_issn=14681218&md5=943b34072b9beb1d50e2818a41b4ace6" title="Click to view the MathML source">R∖{0}class="mathContainer hidden">class="mathCode">$\mathbb{R}\setminus \left\{0\right\}$ (singular) which are infinitesimal at infinity, discussing also their asymptotic behavior. The phenomena we find are present only if absorption and production coexist, i.e., if the reaction term changes sign. Our results are then generalized to include the case where Hardy potentials are considered.