期刊
JOURNAL OF EVOLUTION EQUATIONS
卷 20, 期 2, 页码 375-401出版社
SPRINGER BASEL AG
DOI: 10.1007/s00028-019-00526-4
关键词
Growth-fragmentation equation; Uniform asynchronous exponential growth; Positive semigroups; Quasi-compactness; Creation of moments
The objective is to prove the asynchronous exponential growth of the growth-fragmentation equation in large weighted L1spaces and under general assumptions on the coefficients. The key argument is the creation of moments for the solutions to the Cauchy problem, resulting from the unboundedness of the total fragmentation rate. It allows us to prove the quasi-compactness of the associated (rescaled) semigroup, which in turn provides the exponential convergence toward the projector on the Perron eigenfunction.
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