English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study the existence and multiplicity of solutions of the following freeboundary problem $$ (P)\left\{ \begin{array}{rcll} \del u &=& \lam ( \eps+(1-\eps ) H(u-\mu))~ \hspace{3mm}&\text{in}~\Omega (t)\\ u&=&\overline{u}_{\infty}~\hspace{3mm} &\text{on } ~ \partial \Omega(t) \end{array}\right. $$ where $\Omega(t) \subset \RR^3$ a regular domain at $t>0$,$\eps,~\overline{u}_{\infty},~\lambda,~\mu$ are a positive parameters and $H$is the Heaviside step function. \\The problem (P) has two free boundaries: theouter boundary of $\Omega(t)$ and the inner boundary whose evolution isimplicit generated by the discontinuous nonlinearity $H$. The problem (P) arisein tumor growth models as well as in other contexts such as climatology. First,we show the existence and multiplicity of radial solutions of problem (P) where$\Omega(t)$ is a spherical domain. Moreover, the bifurcation diagrams aregiving. Secondly, using the perturbation technic combining to local methods, weprove the existence of solutions and characterize the free boundaries ofproblem (P) near the corresponding radial solutions.

Perturbation analysis in a free boundary problem arising in tumor growth model