On the influence of diffusion on the competition between bacteria and innate immune system of invertebrates

Adams R.: Sobolev Spaces. 1st edn. Academic Press, New York (1975)

Bassler B.: How bacteria talk to each other: regulation of gene expression by quorum sensing. Curr. Opin. Microbiol. 2, 582 (1999)

Cantrell R., Cosner C.: Spatial Ecology via Reaction-diffusion Equations. Wiley, Chichester (2004)

Cerasuolo, M., Fergola, P., Rionero, S.: On the dynamics of a binary model for the competition between bacteria and innate immune system. In: Ciarletta, M., Fabrizio, M., Morro, A., Rionero, S. (eds.) Proceedings of the International Conference “New Trends in Fluid and Solid Models”. World Scientific, pp. 27–35 (2009)

Evans L.: Partial Differential Equations, vol. 19. AMS, Berkeley (1997)

Fergola, P., Zhang, J., Cerasuolo, M., Ma, Z.: On the influence of quorum sensing in the competition between bacteria and immune system of invertebrates. In: Proceedings of the BIOCOMP2007. Vietri sul Mare, Italy, 24–28 Sept 2007, pp. 215–232 (2008)

Flavin J., Rionero S.: Qualitative Estimates for Partial Differential Equations. 1st edn. CRC Press, Boca Raton, FL (1996)

Iwanaga S., Lee B.L.: Recent advances in the innate immunity of invertebrate animals. J. Biochem. Mol. Biol. 38(2), 128–150 (2005)

McDougald D., Rice S., Kjelleberg S.: Bacterial quorum sensing and interference by naturally occurring biomimics. Anal. Bioanal. Chem. 387, 445–453 (2007)

Protter M., Weinberger H.: Maximum Principles in Differential Equations. Prentice-Hall, Englewood Cliffs, NJ (1967)

Rionero S.: L2 stability of the solutions to a nonlinear binary reaction-diffusion system of p.d.es. Rend. Accad. Naz. Lincei Serie IX, XVI, 227–238 (2005)

Rionero S.: A rigorous reduction of the L2-stability of the solutions to a nonlinear binary reaction-diffusion system of p.d.es. to the stability of the solutions to a linear binary system of o.d.es. J. Math. Anal. Appl. 319, 377–397 (2006)

Rionero S.: Fluid Motion in Porous Media—Lecture Notes of the PHD School of Mathematics and Informatics. University Federico II of Naples, Italy (2008)

Wagner V., Frelinger J., Barth R., Iglewski B.: Quorum sensing: dynamic response of pseudomonas aeruginosa to external signals. Trends. Microbiol. 14, 55–58 (2006)