Asymptotics of semigroups generated by operator matrices

Mugnolo, Delio

doi:10.1007/s40065-014-0107-4

Cited by 8 publications

(3 citation statements)

References 47 publications

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“…Hence, W 0 (G) contains such vectors of functions that are twice weakly differentiable on each edge and continuous in the vertices with Dirichlet boundary conditions. By [45,Cor. 3.6],…”

Section: Definition 41 We Denote Bymentioning

confidence: 97%

Stochastic reaction–diffusion equations on networks

Kovács

Sikolya

2021

J. Evol. Equ.

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We consider stochastic reaction–diffusion equations on a finite network represented by a finite graph. On each edge in the graph, a multiplicative cylindrical Gaussian noise-driven reaction–diffusion equation is given supplemented by a dynamic Kirchhoff-type law perturbed by multiplicative scalar Gaussian noise in the vertices. The reaction term on each edge is assumed to be an odd degree polynomial, not necessarily of the same degree on each edge, with possibly stochastic coefficients and negative leading term. We utilize the semigroup approach for stochastic evolution equations in Banach spaces to obtain existence and uniqueness of solutions with sample paths in the space of continuous functions on the graph. In order to do so, we generalize existing results on abstract stochastic reaction–diffusion equations in Banach spaces.

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“…Hence, W 0 (G) contains such vectors of functions that are twice weakly differentiable on each edge and continuous in the vertices with Dirichlet boundary conditions. By [45,Cor. 3.6],…”

Section: Definition 41 We Denote Bymentioning

confidence: 97%

Stochastic reaction–diffusion equations on networks

Kovács

Sikolya

2021

J. Evol. Equ.

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“…Van Neerven [44]. In [38], the stability of two-coupled systems of PDE's is shown. Recently, in order to face the third order Moore-Gibson-Thompson equation, the authors study such equation as a first order system whose associated operator matrix generates a exponentially stable semigroup on a Hilbert space, see [26].…”

Section: <mentioning

confidence: 99%

Uniform stability for fractional Cauchy problems and applications

Abadías¹,

Álvarez²

2018

TMNA

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In this paper we give uniform stable spatial bounds for the resolvent operator families of the abstract fractional Cauchy problem on R+. Such bounds allow to prove existence and uniqueness of µ-pseudo almost automorphic ✏-mild regular solutions to the nonlinear fractional Cauchy problem in the whole real line. Finally, we apply our main results to the fractional heat equation with critical nonlinearities.

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“…Therefore, based on the symmetry of the numerical range, we consider the semigroup generation of infinite dimensional Hamiltonian operators. The classical results for operator matrices to generate C 0 semigroups are discussed in the diagonal domain by means of standard perturbation theorems, under the assumption that the diagonal elements generate semigroups [9,10]. Note that we are concerned with the Hamiltonian operator with an off-diagonal domain and discuss the core of its off-diagonal elements.…”

Section: Introductionmentioning

confidence: 99%