The solution $u$ of the well-posed problem $$ \begin{cases} \frac{\partial u}{\partial t} =\sum\limits_{i,j=1}^N \partial_i (a_{ij}(x)\partial_j u), &(x,t)\in\Omega\times [0,+\infty),\\ u(x,0)=f(x), & x\in\Omega,\\ \sum\limits_{i,j=1}^N \partial_i (a_{ij}(x)\partial_j u)+\beta (x)\sum\limits_{i,j=1}^N a_{ij}(x)\partial_j u \, n_i+\gamma (x) u-q\beta(x)\Delta_{LB}u=0,& (x,t)\in \partial\Omega\times [0,+\infty), \end{cases} $$ depends continuously on $(a_{ij},\beta,\gamma,q)$.

Continuous dependence on the boundary conditions for the Wentzell Laplacian / Coclite, Giuseppe Maria; A., Favini; G. R., Goldstein; J. A., Goldstein; Romanelli, S.. - In: SEMIGROUP FORUM. - ISSN 0037-1912. - 77:1(2008), pp. 101-108. [10.1007/s00233-008-9068-2]

Continuous dependence on the boundary conditions for the Wentzell Laplacian

COCLITE, Giuseppe Maria;
2008-01-01

Abstract

The solution $u$ of the well-posed problem $$ \begin{cases} \frac{\partial u}{\partial t} =\sum\limits_{i,j=1}^N \partial_i (a_{ij}(x)\partial_j u), &(x,t)\in\Omega\times [0,+\infty),\\ u(x,0)=f(x), & x\in\Omega,\\ \sum\limits_{i,j=1}^N \partial_i (a_{ij}(x)\partial_j u)+\beta (x)\sum\limits_{i,j=1}^N a_{ij}(x)\partial_j u \, n_i+\gamma (x) u-q\beta(x)\Delta_{LB}u=0,& (x,t)\in \partial\Omega\times [0,+\infty), \end{cases} $$ depends continuously on $(a_{ij},\beta,\gamma,q)$.
2008
http://link.springer.com/article/10.1007%2Fs00233-008-9068-2
Continuous dependence on the boundary conditions for the Wentzell Laplacian / Coclite, Giuseppe Maria; A., Favini; G. R., Goldstein; J. A., Goldstein; Romanelli, S.. - In: SEMIGROUP FORUM. - ISSN 0037-1912. - 77:1(2008), pp. 101-108. [10.1007/s00233-008-9068-2]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/93815
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