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pro vyhledávání: '"COLOMBINI, FERRUCCIO"'
In the present paper, we consider second order strictly hyperbolic linear operators of the form $Lu\,=\,\partial_t^2u\,-\,{\rm div}\big(A(t,x)\nabla u\big)$, for $(t,x)\in[0,T]\times\mathbb{R}^n$. We assume the coefficients of the matrix $A(t,x)$ to
Externí odkaz:
http://arxiv.org/abs/2301.10854
We give sufficient conditions for the well-posedness in $\mathcal{C}^\infty$ of the Cauchy problem for third order equations with time dependent coefficients.
Externí odkaz:
http://arxiv.org/abs/2112.04372
In this note we prove a well-posedness result, without loss of derivatives, for strictly hyperbolic wave operators having coefficients which are Zygmund-continuous in the time variable and Lipschitz-continuous in the space variables. The proof is bas
Externí odkaz:
http://arxiv.org/abs/2001.09202
This paper studies the Cauchy problem for variable coefficient weakly hyperbolic first order systems of partial differential operators. The hyperbolicity assumption is that for each $t, x$ the principal symbol is hyperbolic. No hypothesis is imposed
Externí odkaz:
http://arxiv.org/abs/1911.02135
We consider the Cauchy problem for second order differential operators with two independent variables $P=D_t^2-D_x(b(t)a(x))D_x$. Assume that $b(t)$ is a nonnegative $C^{n,alpha}$ function and $a(x)$ is a nonnegative Gevrey function of order $s>1$ we
Externí odkaz:
http://arxiv.org/abs/1712.05253
Autor:
Colombini, Ferruccio, Petkov, Vesselin
Let $V(t) = e^{tG_b},\: t \geq 0,$ be the semigroup generated by Maxwell's equations in an exterior domain $\Omega \subset {\mathbb R}^3$ with dissipative boundary condition $E_{tan}- \gamma(x) (\nu \wedge B_{tan}) = 0, \gamma(x) > 0, \forall x \in \
Externí odkaz:
http://arxiv.org/abs/1705.09583
Publikováno v:
Indiana University Mathematics Journal, 2020 Jan 01. 69(3), 785-836.
Externí odkaz:
https://www.jstor.org/stable/26959653
The present paper concerns the well-posedness of the Cauchy problem for microlocally symmetrizable hyperbolic systems whose coefficients and symmetrizer are log-Lipschitz continuous, uniformly in time and space variables. For the global in space prob
Externí odkaz:
http://arxiv.org/abs/1610.03884
Publikováno v:
In Journal of Differential Equations 25 January 2021 272:222-254
Let $V(t) = e^{tG_b},\: t \geq 0,$ be the semigroup generated by Maxwell's equations in an exterior domain $\Omega \subset {\mathbb R}^3$ with dissipative boundary condition $E_{tan}- \gamma(x) (\nu \wedge B_{tan}) = 0, \gamma(x) > 0, \forall x \in \
Externí odkaz:
http://arxiv.org/abs/1506.02555