Naslov
On principal eigenvalue of stationary diffusion problem with nonsymmetric coefficients

Autori
Vrdoljak, Marko

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Izvornik
Proceedings of the Conference on Applied Mathematics and Scientific Computing / Drmač, Zlatko ; Hari, Vjeran ; Sopta, Luka ; Tutek, Zvonimir ; Veselić, Krešimir - New York (NY) : Kluwer Academic Publishers ; Plenum Publishers, 2003, 313-322

ISBN
0-306-47426-3

Skup
Conference on Applied Mathematics and Scientific Computing

Mjesto i datum
Brijuni, Hrvatska, 23.06.2003. - 27.06.2003

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
stationary diffusion; principal eigenvalue; H-topology; singular values

Sažetak
We consider the eigenvalue problem $$ \left\{; \begin{;array};{;l}; -\dv(A\nabla u)=\lambda\rho u\\ u\in {;\rm H};^1_0(\Omega)\\ \end{;array}; \right. $$ where $\Omega\in{;\bf R};^d$ is open and bounded, $\rho\in{;\rm L};^\infty(\Omega)$ and $A\in{;\rm L};^\infty(\Omega ; {;\rm M};_{;d\times d};)$ satisfying $$ A(x)\xi\cdot\xi\geq\alpha\xi\cdot\xi\ , \quad\rho(x)\geq c\, , \qquad \xi\in{;\bf R};^d, \, {;\rm a.e.};\ x\in\Omega\, , $$ for some $\alpha, c>0$. We show that, under appropriate conditions on smoothness of coefficients, the principal eigenvalue depends continuously on coefficients with respect to H-topology for $A$ and L$^\infty$ weak $\ast$ topology for $\rho$. An application of this result in optimal shape design problem of optimising the principal eigenvalue is presented. Moreover, in the same topology for coefficients, we obtain the continuity of corresponding singular values.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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