RT journal article
T1 Increase of power leads to a bilateral solution to a strongly nonlinear elliptic coupled system
A1 Ortegón Gallego, Francisco
A1 Rhoudaf, Mohamed
A1 Talbi, Hajar
A2 Matemáticas
K1 coupled system
K1 bilateral solution
K1 nonlinear elliptic equation
K1 thermistor problem
K1 penalization techniques
AB In this paper, we analyze the following nonlinear elliptic problem A (u) = ρ (u) | φ | 2 in ω, div (ρ (u) φ) = 0 in ω, u = 0 on ω, φ = φ 0 on ω. $\begin{cases}A\left(u\right)=\rho \left(u\right)\vert \nabla \varphi {\vert }^{2}\,\text{in}\,{\Omega},\quad \hfill \\ \text{div}\left(\rho \left(u\right)\nabla \varphi \right)=0\,\text{in}\,{\Omega},\quad \hfill \\ u=0\,\text{on}\,\partial {\Omega},\quad \hfill \\ \varphi ={\varphi }_{0}\,\text{on}\,\partial {\Omega}.\quad \hfill \end{cases}$ where A(u) = -diva(x, u, u) is a Leray-Lions operator of order p. The second member of the first equation is only in L 1(ω). We prove the existence of a bilateral solution by an approximation procedure, the keypoint being a penalization technique.
PB DE GRUYTER POLAND
SN 2169-0375
YR 2024
FD 2024
LK http://hdl.handle.net/10498/33723
UL http://hdl.handle.net/10498/33723
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 11-nov-2026