Naslov
On principal eigenvalue of stationary diffusion problem with nonsymmetric coefficients

Autori
Vrdoljak, Marko

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Applied Mathematics and Scientific computing / Drmač, Z.; Hari V.; Sopta L.; Tutek Z.; Veselić K. - Zagreb : Matematički odsjek Prirodoslovno-matematičkog fakulteta Sveučilišta u Zagrebu, 2001, 26-27

Skup
Applied Mathematics and Scientific computing

Mjesto i datum
Dubrovnik, Hrvatska, 04.06.2001. - 08.06.2001

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
principal eigenvalue; homogenisation; stationary diffusion

Sažetak
We consider the eigenvalue problem $$ \left\{\eqalign{ -&\rm{ div} ({\bf A}\nabla u)=\lambda\rho u\cr &u\in {\rm H}^1_0(\Omega)\cr } \right. $$ where $\Omega\in{\bf R}^d$ is open and bounded, $\rho\in{\rm L}^\infty(\Omega)$ and ${\bf A}\in{\rm L}^\infty(\Omega;{\rm M}_{d\times d})$ satisfying $$ {\bf A}(x)\xi\cdot\xi\geq\alpha\xi\cdot\xi\,\quad\rho(x)\geq c\,,\qquad \xi\in{\bf R}^d, \ ,{\rm a.e.}\x\in\Omega $$ for some $\alpha, c>0$. Using the strong maximum principle, obtained by Harnack's inequality, and Krein-Rutman's th eorem, the existence of principle eigenvalue is proved. Moreover, under appropriate conditions, the pr incipal eigenvalue depends continuously on coefficients with respect to H-topology for ${\b f A}$ and L$^\infty$ weak $\ast$ topology for $\rho$.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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