Irregular convergence of mild solutions of semilinear equations
Copyright policy )Irregular convergence of mild solutions of semilinear equations
We prove that even irregular convergence of semigroups of operators implies similar convergence of mild solutions of the related semi-linear equations with Lipschitz continuous nonlinearity. This result is then applied to three models originating from mathematical biology: shadow systems, diffusions on thin layers, and dynamics of neurotransmitters
21 pages, no figures. Minor revision: Some typos fixed
- University of Konstanz Germany
- Lublin University of Technology Poland
thin layers, 35K57, 47D06, 35B25, 35K58, semi-linear equations, Nonlinear differential equations in abstract spaces, semigroups of operators, signaling pathways, Functional Analysis (math.FA), Mathematics - Functional Analysis, Mathematics - Analysis of PDEs, FOS: Mathematics, singular perturbations, shadow systems, Analysis of PDEs (math.AP)
thin layers, 35K57, 47D06, 35B25, 35K58, semi-linear equations, Nonlinear differential equations in abstract spaces, semigroups of operators, signaling pathways, Functional Analysis (math.FA), Mathematics - Functional Analysis, Mathematics - Analysis of PDEs, FOS: Mathematics, singular perturbations, shadow systems, Analysis of PDEs (math.AP)
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