TY - JOUR

T1 - Global existence in reaction-diffusion systems with mass control under relaxed assumptions merely referring to cross-absorptive effects

AU - Lankeit, Johannes

AU - Winkler, Michael

N1 - Funding Information: The authors warmly thank the anonymous reviewers for their thorough evaluation in all details, and for numerous helpful comments which have led to substantial improvement. Apart from that, the second author acknowledges support of the Deutsche Forschungsgemeinschaft in the context of the project Emergence of structures and advantages in cross-diffusion systems (No. 411007140, GZ: WI 3707/5-1).

PY - 2022/3/2

Y1 - 2022/3/2

N2 - We introduce a generalized concept of solutions for reaction-diffusion systems and prove their global existence. The only restriction on the reaction function beyond regularity, quasipositivity and mass control is special in that it merely controls the growth of cross-absorptive terms. The result covers nonlinear diffusion and does not rely on an entropy estimate.

AB - We introduce a generalized concept of solutions for reaction-diffusion systems and prove their global existence. The only restriction on the reaction function beyond regularity, quasipositivity and mass control is special in that it merely controls the growth of cross-absorptive terms. The result covers nonlinear diffusion and does not rely on an entropy estimate.

KW - math.AP

KW - 35K57, 35D99, 35K59

KW - Reaction–diffusion equation

KW - Global existence

KW - Renormalized solution

UR - http://www.scopus.com/inward/record.url?scp=85126048423&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2108.00673

DO - 10.48550/arXiv.2108.00673

M3 - Article

VL - 22

JO - Journal of Evolution Equations

JF - Journal of Evolution Equations

SN - 1424-3199

IS - 1

M1 - 14

ER -