FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2892221214> ?p ?o ?g. }

• W2892221214 endingPage "40" @default.
• W2892221214 startingPage "15" @default.
• W2892221214 abstract "We consider the following Cauchy problem for a wave equation with time-dependent damping term b(t)ut and mass term m(t)2u, and a power nonlinearity |u|p: utt−Δu+b(t)ut+m2(t)u=|u|p,t≥0,x∈Rn,u(0,x)=f(x),ut(0,x)=g(x).We discuss how the interplay between an effective time-dependent damping term and a time-dependent mass term influences the decay rate of the solution to the corresponding linear Cauchy problem, in the case in which the mass is dominated by the damping term, i.e. m(t)=o(b(t)) as t→∞. Then we use the obtained estimates of solutions to linear Cauchy problems to prove the existence of global in-time energy solutions to the Cauchy problem with power nonlinearity |u|p at the right-hand side of the equation, in a supercritical range p>p̄, assuming small data in the energy space (f,g)∈H1×L2. In particular, we find a threshold case for the behavior of m(t) with respect to b(t). Below the threshold, the mass has no influence on the critical exponent, so that p̄=1+4∕n, as in the case with m=0. Above the threshold, p̄=1, global (in time) small data energy solutions exist for any p>1, as it happens for the classical damped Klein–Gordon equation (b=m=1). Along the threshold, varying a parameter β∈[0,∞] which depends on the behavior of m(t) with respect to b(t), we find a scale of critical exponents, namely, p̄=1+4∕(n+4β). This scale of critical exponents is consistent with the diffusion phenomenon, that is, it is the same scale of critical exponents of the Cauchy problem for the corresponding diffusive equation −Δv+b(t)vt+m2(t)v=|v|p,t≥0,x∈Rn,v(0,x)=φ(x)." @default.
• W2892221214 created "2018-09-27" @default.
• W2892221214 creator A5001308092 @default.
• W2892221214 creator A5035090882 @default.
• W2892221214 creator A5068520014 @default.
• W2892221214 date "2019-02-01" @default.
• W2892221214 modified "2023-09-27" @default.
• W2892221214 title "A scale of critical exponents for semilinear waves with time-dependent damping and mass terms" @default.
• W2892221214 cites W1965849331 @default.
• W2892221214 cites W1966382600 @default.
• W2892221214 cites W2011540258 @default.
• W2892221214 cites W2017153447 @default.
• W2892221214 cites W2023143510 @default.
• W2892221214 cites W2030876627 @default.
• W2892221214 cites W2048877476 @default.
• W2892221214 cites W2065988506 @default.
• W2892221214 cites W2077221631 @default.
• W2892221214 cites W2093294756 @default.
• W2892221214 cites W2116411303 @default.
• W2892221214 cites W2144545313 @default.
• W2892221214 cites W2319319158 @default.
• W2892221214 cites W2325401968 @default.
• W2892221214 cites W2414896950 @default.
• W2892221214 cites W2511506735 @default.
• W2892221214 cites W261300459 @default.
• W2892221214 cites W2917169291 @default.
• W2892221214 cites W2963099303 @default.
• W2892221214 cites W3102817781 @default.
• W2892221214 cites W3204681790 @default.
• W2892221214 doi "https://doi.org/10.1016/j.na.2018.08.006" @default.
• W2892221214 hasPublicationYear "2019" @default.
• W2892221214 type Work @default.
• W2892221214 sameAs 2892221214 @default.
• W2892221214 citedByCount "7" @default.
• W2892221214 countsByYear W28922212142019 @default.
• W2892221214 countsByYear W28922212142020 @default.
• W2892221214 countsByYear W28922212142021 @default.
• W2892221214 countsByYear W28922212142022 @default.
• W2892221214 crossrefType "journal-article" @default.
• W2892221214 hasAuthorship W2892221214A5001308092 @default.
• W2892221214 hasAuthorship W2892221214A5035090882 @default.
• W2892221214 hasAuthorship W2892221214A5068520014 @default.
• W2892221214 hasConcept C121332964 @default.
• W2892221214 hasConcept C134306372 @default.
• W2892221214 hasConcept C138885662 @default.
• W2892221214 hasConcept C149288129 @default.
• W2892221214 hasConcept C153635880 @default.
• W2892221214 hasConcept C158622935 @default.
• W2892221214 hasConcept C159985019 @default.
• W2892221214 hasConcept C164154869 @default.
• W2892221214 hasConcept C192562407 @default.
• W2892221214 hasConcept C204323151 @default.
• W2892221214 hasConcept C26955809 @default.
• W2892221214 hasConcept C2778572836 @default.
• W2892221214 hasConcept C2780388253 @default.
• W2892221214 hasConcept C33923547 @default.
• W2892221214 hasConcept C37914503 @default.
• W2892221214 hasConcept C41895202 @default.
• W2892221214 hasConcept C49344536 @default.
• W2892221214 hasConcept C59696629 @default.
• W2892221214 hasConcept C61797465 @default.
• W2892221214 hasConcept C62520636 @default.
• W2892221214 hasConceptScore W2892221214C121332964 @default.
• W2892221214 hasConceptScore W2892221214C134306372 @default.
• W2892221214 hasConceptScore W2892221214C138885662 @default.
• W2892221214 hasConceptScore W2892221214C149288129 @default.
• W2892221214 hasConceptScore W2892221214C153635880 @default.
• W2892221214 hasConceptScore W2892221214C158622935 @default.
• W2892221214 hasConceptScore W2892221214C159985019 @default.
• W2892221214 hasConceptScore W2892221214C164154869 @default.
• W2892221214 hasConceptScore W2892221214C192562407 @default.
• W2892221214 hasConceptScore W2892221214C204323151 @default.
• W2892221214 hasConceptScore W2892221214C26955809 @default.
• W2892221214 hasConceptScore W2892221214C2778572836 @default.
• W2892221214 hasConceptScore W2892221214C2780388253 @default.
• W2892221214 hasConceptScore W2892221214C33923547 @default.
• W2892221214 hasConceptScore W2892221214C37914503 @default.
• W2892221214 hasConceptScore W2892221214C41895202 @default.
• W2892221214 hasConceptScore W2892221214C49344536 @default.
• W2892221214 hasConceptScore W2892221214C59696629 @default.
• W2892221214 hasConceptScore W2892221214C61797465 @default.
• W2892221214 hasConceptScore W2892221214C62520636 @default.
• W2892221214 hasLocation W28922212141 @default.
• W2892221214 hasOpenAccess W2892221214 @default.
• W2892221214 hasPrimaryLocation W28922212141 @default.
• W2892221214 hasRelatedWork W1852872935 @default.
• W2892221214 hasRelatedWork W1987232319 @default.
• W2892221214 hasRelatedWork W1998906527 @default.
• W2892221214 hasRelatedWork W2057055378 @default.
• W2892221214 hasRelatedWork W2079059539 @default.
• W2892221214 hasRelatedWork W2115056868 @default.
• W2892221214 hasRelatedWork W2392831892 @default.
• W2892221214 hasRelatedWork W2587044388 @default.
• W2892221214 hasRelatedWork W3103143069 @default.
• W2892221214 hasRelatedWork W3126711774 @default.
• W2892221214 hasVolume "179" @default.
• W2892221214 isParatext "false" @default.
• W2892221214 isRetracted "false" @default.

• next