We study the rate of
convergence of global attractors and eigenvalues of the
family of dissipative
semilinear wave equations with variable coefficients $u_{tt}+\Lambda_\epsilon
u+\Lambda_\epsilon^{\delta}u_t=f(u)$, where $\Lambda_\epsilon$ is
the elliptic operator $-\operatorname{div} (a_\epsilon(x)\nabla)$ with $\epsilon \in
[0,1]$ and sufficiently smooth coefficients $a_\epsilon$, and
where $\delta\in\big(\frac12,1\big)$
and the nonlinearity $f$ is a continuously differentiable function
satisfying suitable growth conditions. We show that the rate of convergence,
as $\epsilon\to0^+$, of the global attractors of these problems, as well
as of their eigenvalues, is proportional to the distance of the coefficients
$\|a_\epsilon-a_0\|_{L^\infty(\Omega)}$.

We study the rate of
convergence of global attractors and eigenvalues of the
family of dissipative
semilinear wave equations with variable coefficients $u_{tt}+\Lambda_\epsilon
u+\Lambda_\epsilon^{\delta}u_t=f(u)$, where $\Lambda_\epsilon$ is
the elliptic operator $-\operatorname{div} (a_\epsilon(x)\nabla)$ with $\epsilon \in
[0,1]$ and sufficiently smooth coefficients $a_\epsilon$, and
where $\delta\in\big(\frac12,1\big)$
and the nonlinearity $f$ is a continuously differentiable function
satisfying suitable growth conditions. We show that the rate of convergence,
as $\epsilon\to0^+$, of the global attractors of these problems, as well
as of their eigenvalues, is proportional to the distance of the coefficients
$\|a_\epsilon-a_0\|_{L^\infty(\Omega)}$.

We study the rate of
convergence of global attractors and eigenvalues of the
family of dissipative
semilinear wave equations with variable coefficients $u_{tt}+\Lambda_\epsilon
u+\Lambda_\epsilon^{\delta}u_t=f(u)$, where $\Lambda_\epsilon$ is
the elliptic operator $-\operatorname{div} (a_\epsilon(x)\nabla)$ with $\epsilon \in
[0,1]$ and sufficiently smooth coefficients $a_\epsilon$, and
where $\delta\in\big(\frac12,1\big)$
and the nonlinearity $f$ is a continuously differentiable function
satisfying suitable growth conditions. We show that the rate of convergence,
as $\epsilon\to0^+$, of the global attractors of these problems, as well
as of their eigenvalues, is proportional to the distance of the coefficients
$\|a_\epsilon-a_0\|_{L^\infty(\Omega)}$.

We study the rate of
convergence of global attractors and eigenvalues of the
family of dissipative
semilinear wave equations with variable coefficients $u_{tt}+\Lambda_\epsilon
u+\Lambda_\epsilon^{\delta}u_t=f(u)$, where $\Lambda_\epsilon$ is
the elliptic operator $-\operatorname{div} (a_\epsilon(x)\nabla)$ with $\epsilon \in
[0,1]$ and sufficiently smooth coefficients $a_\epsilon$, and
where $\delta\in\big(\frac12,1\big)$
and the nonlinearity $f$ is a continuously differentiable function
satisfying suitable growth conditions. We show that the rate of convergence,
as $\epsilon\to0^+$, of the global attractors of these problems, as well
as of their eigenvalues, is proportional to the distance of the coefficients
$\|a_\epsilon-a_0\|_{L^\infty(\Omega)}$.

We study the rate of
convergence of global attractors and eigenvalues of the
family of dissipative
semilinear wave equations with variable coefficients $u_{tt}+\Lambda_\epsilon
u+\Lambda_\epsilon^{\delta}u_t=f(u)$, where $\Lambda_\epsilon$ is
the elliptic operator $-\operatorname{div} (a_\epsilon(x)\nabla)$ with $\epsilon \in
[0,1]$ and sufficiently smooth coefficients $a_\epsilon$, and
where $\delta\in\big(\frac12,1\big)$
and the nonlinearity $f$ is a continuously differentiable function
satisfying suitable growth conditions. We show that the rate of convergence,
as $\epsilon\to0^+$, of the global attractors of these problems, as well
as of their eigenvalues, is proportional to the distance of the coefficients
$\|a_\epsilon-a_0\|_{L^\infty(\Omega)}$.

We study the rate of
convergence of global attractors and eigenvalues of the
family of dissipative
semilinear wave equations with variable coefficients $u_{tt}+\Lambda_\epsilon
u+\Lambda_\epsilon^{\delta}u_t=f(u)$, where $\Lambda_\epsilon$ is
the elliptic operator $-\operatorname{div} (a_\epsilon(x)\nabla)$ with $\epsilon \in
[0,1]$ and sufficiently smooth coefficients $a_\epsilon$, and
where $\delta\in\big(\frac12,1\big)$
and the nonlinearity $f$ is a continuously differentiable function
satisfying suitable growth conditions. We show that the rate of convergence,
as $\epsilon\to0^+$, of the global attractors of these problems, as well
as of their eigenvalues, is proportional to the distance of the coefficients
$\|a_\epsilon-a_0\|_{L^\infty(\Omega)}$.

Keywords

wave equations, variable coefficients, global attractors,
rates of convergence