Universität zu Köln

Drewitz, Alexander ORCID: 0000-0002-5546-3614 and Schmitz, Lars (2022). Invariance Principles and Log-Distance of F-KPP Fronts in a Random Medium. Arch. Ration. Mech. Anal., 246 (2-3). S. 877 - 956. NEW YORK: SPRINGER. ISSN 1432-0673

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Abstract

We study the front of the solution to the F-KPP equation with randomized non-linearity. Under suitable assumptions on the randomness including spatial mixing behavior and boundedness, we show that the front of the solution lags at most logarithmically in time behind the front of the solution of the corresponding linearized equation, i.e. the parabolic Anderson model. This can be interpreted as a partial generalization of Bramson's findings (Bramson in Commun Pure Appl Math 31(5):531-581, 1978) for the homogeneous setting. Partially building on this result and its derivation, we establish functional central limit theorems for the fronts of the solutions to both equations.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Drewitz, Alexander UNSPECIFIED orcid.org/0000-0002-5546-3614 UNSPECIFIED Schmitz, Lars UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-656723
DOI:	10.1007/s00205-022-01824-x
Journal or Publication Title:	Arch. Ration. Mech. Anal.
Volume:	246
Number:	2-3
Page Range:	S. 877 - 956
Date:	2022
Publisher:	SPRINGER
Place of Publication:	NEW YORK
ISSN:	1432-0673
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language PROPAGATION; CONVERGENCE; EQUATION; WAVES Multiple languages Mathematics, Applied; Mechanics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/65672