Matches in SemOpenAlex for { <https://semopenalex.org/work/W2810761244> ?p ?o ?g. }
- W2810761244 endingPage "R239" @default.
- W2810761244 startingPage "R189" @default.
- W2810761244 abstract "Localized spatial patterns commonly occur for various classes of linear and nonlinear diffusive processes. In particular, localized spot patterns, where the solution concentrates at discrete points in the domain, occur in the nonlinear reaction–diffusion (RD) modeling of diverse phenomena such as chemical patterns, biological morphogenesis, and the spatial distribution of urban crime. In a 2D spatial domain we survey some recent and new results for the existence, linear stability, and slow dynamics of localized spot patterns by using the Brusselator RD model as the prototypical example. In the context of linear diffusive systems with localized solution behavior, we will discuss some previous results for the determination of the mean first capture time for a Brownian particle in a 2D domain with localized traps, and the determination of the persistence threshold of a species in a 2D landscape with patchy food resources. Common features in the analysis of all of these spatially localized patterns are emphasized, including the key role of certain matrices involving various Green's functions, and the derivation and study of new classes of interacting particle systems and discrete variational problems arising from various asymptotic reductions. The mathematical tools include matched asymptotic analysis based on strong localized perturbation theory, spectral analysis, the analysis of nonlocal eigenvalue problems, and bifurcation theory. Some specific open problems are highlighted and, more broadly, we will discuss a few new research frontiers for the analysis of localized patterns in multi-dimensional domains." @default.
- W2810761244 created "2018-07-10" @default.
- W2810761244 creator A5037517718 @default.
- W2810761244 date "2018-06-28" @default.
- W2810761244 modified "2023-09-25" @default.
- W2810761244 title "Spots, traps, and patches: asymptotic analysis of localized solutions to some linear and nonlinear diffusive systems" @default.
- W2810761244 cites W1501601053 @default.
- W2810761244 cites W1556426368 @default.
- W2810761244 cites W1575714182 @default.
- W2810761244 cites W1608234917 @default.
- W2810761244 cites W1916127968 @default.
- W2810761244 cites W1963942260 @default.
- W2810761244 cites W1966189989 @default.
- W2810761244 cites W1967724962 @default.
- W2810761244 cites W1970212587 @default.
- W2810761244 cites W1971175243 @default.
- W2810761244 cites W1973861336 @default.
- W2810761244 cites W1980661496 @default.
- W2810761244 cites W1986364663 @default.
- W2810761244 cites W1986850658 @default.
- W2810761244 cites W1989095982 @default.
- W2810761244 cites W1990000710 @default.
- W2810761244 cites W1992108660 @default.
- W2810761244 cites W1993433742 @default.
- W2810761244 cites W1993661467 @default.
- W2810761244 cites W1997341646 @default.
- W2810761244 cites W1997790849 @default.
- W2810761244 cites W1998942388 @default.
- W2810761244 cites W1999102797 @default.
- W2810761244 cites W2002181677 @default.
- W2810761244 cites W2005646444 @default.
- W2810761244 cites W2006640177 @default.
- W2810761244 cites W2010588864 @default.
- W2810761244 cites W2012310374 @default.
- W2810761244 cites W2012391347 @default.
- W2810761244 cites W2016633545 @default.
- W2810761244 cites W2024184910 @default.
- W2810761244 cites W2031042504 @default.
- W2810761244 cites W2034779015 @default.
- W2810761244 cites W2035271803 @default.
- W2810761244 cites W2036807344 @default.
- W2810761244 cites W2037127795 @default.
- W2810761244 cites W2037622031 @default.
- W2810761244 cites W2038699288 @default.
- W2810761244 cites W2038975311 @default.
- W2810761244 cites W2041161071 @default.
- W2810761244 cites W2043291304 @default.
- W2810761244 cites W2043302678 @default.
- W2810761244 cites W2047898167 @default.
- W2810761244 cites W2048212809 @default.
- W2810761244 cites W2053012879 @default.
- W2810761244 cites W2060650476 @default.
- W2810761244 cites W2060795153 @default.
- W2810761244 cites W2061708448 @default.
- W2810761244 cites W2064809044 @default.
- W2810761244 cites W2066347815 @default.
- W2810761244 cites W2067573687 @default.
- W2810761244 cites W2073322626 @default.
- W2810761244 cites W2074319891 @default.
- W2810761244 cites W2074890393 @default.
- W2810761244 cites W2080580900 @default.
- W2810761244 cites W2083107946 @default.
- W2810761244 cites W2084881110 @default.
- W2810761244 cites W2086167835 @default.
- W2810761244 cites W2092772931 @default.
- W2810761244 cites W2093708215 @default.
- W2810761244 cites W2094942961 @default.
- W2810761244 cites W2110902335 @default.
- W2810761244 cites W2114942284 @default.
- W2810761244 cites W2118904337 @default.
- W2810761244 cites W2125467086 @default.
- W2810761244 cites W2126716506 @default.
- W2810761244 cites W2129180949 @default.
- W2810761244 cites W2129758174 @default.
- W2810761244 cites W2131000438 @default.
- W2810761244 cites W2137308669 @default.
- W2810761244 cites W2140476512 @default.
- W2810761244 cites W2141542600 @default.
- W2810761244 cites W2143652559 @default.
- W2810761244 cites W2148956121 @default.
- W2810761244 cites W2154380517 @default.
- W2810761244 cites W2165136711 @default.
- W2810761244 cites W2171547389 @default.
- W2810761244 cites W2171934339 @default.
- W2810761244 cites W2253211704 @default.
- W2810761244 cites W2258270384 @default.
- W2810761244 cites W2270410177 @default.
- W2810761244 cites W2313246800 @default.
- W2810761244 cites W2313689636 @default.
- W2810761244 cites W2326835827 @default.
- W2810761244 cites W2334189887 @default.
- W2810761244 cites W2405536608 @default.
- W2810761244 cites W2486477228 @default.
- W2810761244 cites W2570514638 @default.
- W2810761244 cites W2583127447 @default.
- W2810761244 cites W2590845087 @default.
- W2810761244 cites W2592512474 @default.
- W2810761244 cites W2675016913 @default.