Matches in SemOpenAlex for { <https://semopenalex.org/work/W2019882257> ?p ?o ?g. }
Showing items 1 to 100 of
100
with 100 items per page.
- W2019882257 endingPage "1797" @default.
- W2019882257 startingPage "1757" @default.
- W2019882257 abstract "In this paper we develop an intrinsic approach to derivation of energy decay rates for the semilinear wave equation with localized interior nonlinear monotone damping g(ut) and a source term f(u). The proposed approach allows to consider, in an unified way, much more general classes of hyperbolic problems than addressed before in the literature. These generalizations refer to both geometric and topological aspects of the problem. The method leads to optimal decay rates for solutions of semilinear hyperbolic equations driven by a source of critical exponent and subjected to a nonlinear damping localized in a small region adjacent to a portion of the boundary. The distinct features of the model include: (i) Neumann boundary conditions are assumed and, (ii) no growth conditions are imposed on the damping g(s). It is well known that Neumann boundary does not satisfy Lopatinski condition and, therefore, the analysis of propagation of energy in the absence of the damping on the Neumann part of the boundary requires special geometric considerations. In addition, the sole conditions assumed on g(s) are monotonicity, continuity and g(0)=0. In particular, no differentiability and no growth conditions are imposed on the damping both at the origin and at the infinity. The asymptotic decay rates for the energy function are obtained from an intrinsic algorithm driven by solutions of simple ODE. Several examples illustrate the theory by exhibiting various decay rates (exponential, algebraic, rational, logarithmic, etc.) for the energy functional. An important corollary of our energy decay theorem is a stability result which shows that, under certain conditions, when dissipation is sublinear at infinity, the solution of the system remains uniformly bounded for all time in the norms above the finite energy level, even in the presence of a nonlinear source term." @default.
- W2019882257 created "2016-06-24" @default.
- W2019882257 creator A5053756814 @default.
- W2019882257 creator A5078565821 @default.
- W2019882257 date "2006-04-01" @default.
- W2019882257 modified "2023-10-09" @default.
- W2019882257 title "Energy decay rates for the semilinear wave equation with nonlinear localized damping and source terms" @default.
- W2019882257 cites W1597700183 @default.
- W2019882257 cites W1963157654 @default.
- W2019882257 cites W1992941868 @default.
- W2019882257 cites W1995358042 @default.
- W2019882257 cites W2001013647 @default.
- W2019882257 cites W2001156598 @default.
- W2019882257 cites W2007990210 @default.
- W2019882257 cites W2009961626 @default.
- W2019882257 cites W2014171178 @default.
- W2019882257 cites W2023542822 @default.
- W2019882257 cites W2026523808 @default.
- W2019882257 cites W2072193224 @default.
- W2019882257 cites W2081572242 @default.
- W2019882257 cites W2231908444 @default.
- W2019882257 cites W2257184362 @default.
- W2019882257 cites W334868982 @default.
- W2019882257 cites W4230964375 @default.
- W2019882257 cites W4250608538 @default.
- W2019882257 doi "https://doi.org/10.1016/j.na.2005.07.024" @default.
- W2019882257 hasPublicationYear "2006" @default.
- W2019882257 type Work @default.
- W2019882257 sameAs 2019882257 @default.
- W2019882257 citedByCount "106" @default.
- W2019882257 countsByYear W20198822572012 @default.
- W2019882257 countsByYear W20198822572013 @default.
- W2019882257 countsByYear W20198822572014 @default.
- W2019882257 countsByYear W20198822572015 @default.
- W2019882257 countsByYear W20198822572016 @default.
- W2019882257 countsByYear W20198822572017 @default.
- W2019882257 countsByYear W20198822572018 @default.
- W2019882257 countsByYear W20198822572019 @default.
- W2019882257 countsByYear W20198822572020 @default.
- W2019882257 countsByYear W20198822572021 @default.
- W2019882257 countsByYear W20198822572022 @default.
- W2019882257 countsByYear W20198822572023 @default.
- W2019882257 crossrefType "journal-article" @default.
- W2019882257 hasAuthorship W2019882257A5053756814 @default.
- W2019882257 hasAuthorship W2019882257A5078565821 @default.
- W2019882257 hasConcept C105795698 @default.
- W2019882257 hasConcept C121332964 @default.
- W2019882257 hasConcept C134306372 @default.
- W2019882257 hasConcept C158622935 @default.
- W2019882257 hasConcept C163681178 @default.
- W2019882257 hasConcept C167964875 @default.
- W2019882257 hasConcept C180188523 @default.
- W2019882257 hasConcept C182310444 @default.
- W2019882257 hasConcept C185544564 @default.
- W2019882257 hasConcept C186370098 @default.
- W2019882257 hasConcept C202615002 @default.
- W2019882257 hasConcept C33923547 @default.
- W2019882257 hasConcept C39927690 @default.
- W2019882257 hasConcept C59696629 @default.
- W2019882257 hasConcept C62354387 @default.
- W2019882257 hasConcept C62520636 @default.
- W2019882257 hasConcept C72169020 @default.
- W2019882257 hasConceptScore W2019882257C105795698 @default.
- W2019882257 hasConceptScore W2019882257C121332964 @default.
- W2019882257 hasConceptScore W2019882257C134306372 @default.
- W2019882257 hasConceptScore W2019882257C158622935 @default.
- W2019882257 hasConceptScore W2019882257C163681178 @default.
- W2019882257 hasConceptScore W2019882257C167964875 @default.
- W2019882257 hasConceptScore W2019882257C180188523 @default.
- W2019882257 hasConceptScore W2019882257C182310444 @default.
- W2019882257 hasConceptScore W2019882257C185544564 @default.
- W2019882257 hasConceptScore W2019882257C186370098 @default.
- W2019882257 hasConceptScore W2019882257C202615002 @default.
- W2019882257 hasConceptScore W2019882257C33923547 @default.
- W2019882257 hasConceptScore W2019882257C39927690 @default.
- W2019882257 hasConceptScore W2019882257C59696629 @default.
- W2019882257 hasConceptScore W2019882257C62354387 @default.
- W2019882257 hasConceptScore W2019882257C62520636 @default.
- W2019882257 hasConceptScore W2019882257C72169020 @default.
- W2019882257 hasIssue "8" @default.
- W2019882257 hasLocation W20198822571 @default.
- W2019882257 hasOpenAccess W2019882257 @default.
- W2019882257 hasPrimaryLocation W20198822571 @default.
- W2019882257 hasRelatedWork W1525504109 @default.
- W2019882257 hasRelatedWork W2011232312 @default.
- W2019882257 hasRelatedWork W2047053200 @default.
- W2019882257 hasRelatedWork W2514174763 @default.
- W2019882257 hasRelatedWork W2549230023 @default.
- W2019882257 hasRelatedWork W2920286280 @default.
- W2019882257 hasRelatedWork W2964850913 @default.
- W2019882257 hasRelatedWork W2998711696 @default.
- W2019882257 hasRelatedWork W3112793975 @default.
- W2019882257 hasRelatedWork W4298181152 @default.
- W2019882257 hasVolume "64" @default.
- W2019882257 isParatext "false" @default.
- W2019882257 isRetracted "false" @default.
- W2019882257 magId "2019882257" @default.
- W2019882257 workType "article" @default.