Naslov
H-measures and variants applied to parabolic equations

Autori
Antonić, Nenad ; Lazar, Martin

Izvornik
Journal of Mathematical Analysis and Applications (0022-247X) 343 (2008), 1; 207-225

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
H-measures; oscillations; parabolic equation; Schrodinger equation

Sažetak
Since their introduction H-measures have been mostly used in problems related to propagation effects for hyperbolic equations and systems. In this study we give an attempt to apply the H-measure theory to other types of equations. Through a number of examples we present how do the differences between parabolic and hyperbolic equations reflect in the properties of H-measures corresponding to the solutions. Secondly, we apply the H-measures to the Schr\"odinger equation, where we succeed in proving a propagation property. However, our conclusion is that a variant of H-measures should be sought which would be better suited to parabolic problems. We propose such a variant, show some fundamental properties and illustrate its applicability by some examples. In particular, we show that the variant provides new information in a number of situations where the original H-measures did not. Finally, we describe how the new variant can be used in small amplitude homogenisation of parabolic equations.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA