Semilinear formulation of a hyperbolic system of partial differential equations
Barril, Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Calsina i Ballesta, Àngel (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Data:	2022
Resum:	In this paper, we solve the Cauchy problem for a hyperbolic system of first-order PDEs defined on a certain Banach space X. The system has a special semilinear structure because, on the one hand, the evolution law can be expressed as the sum of a linear unbounded operator and a nonlinear Lipschitz function but, on the other hand, the nonlinear perturbation takes values not in X but on a larger space Y which is related to X. In order to deal with this situation we use the theory of dual semigroups. Stability results around steady states are also given when the nonlinear perturbation is Fréchet differentiable. These results are based on two propositions: one relating the local dynamics of the nonlinear semiflow with the linearised semigroup around the equilibrium, and a second relating the dynamical properties of the linearised semigroup with the spectral values of its generator. The later is proven by showing that the Spectral Mapping Theorem always applies to the semigroups one obtains when the semiflow is linearised. Some epidemiological applications involving gut bacteria are commented.
Ajuts:	Agencia Estatal de Investigación MTM2014-52402-C03-2P Agencia Estatal de Investigación MTM2017-84214-C2-2-P Ministerio de Educación, Cultura y Deporte FPU13/04333
Nota:	Altres ajuts: acords transformatius de la UAB
Drets:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Semilinear hyperbolic systems ; Sun dual formulation ; Linearization principle ; Spectral mapping theorem ; Spatially structured populations
Publicat a:	Journal of Evolution Equations, Vol. 22, Issue 3 (September 2022) , art. 58, ISSN 1424-3202

DOI: 10.1007/s00028-022-00816-4

33 p, 500.8 KB

El registre apareix a les col·leccions:
Articles > Articles de recerca
Articles > Articles publicats