Singular limit of differential systems with memory
Monica ContiVittorino PataMarco Squassina
35B2535B4035K5737L3045K05equations with memorysingular limitstrongly continuous semigroupsglobal attractorsrobust exponential attractors
We consider differential systems with memory terms, expressed by convolution integrals, which account for the past history of one or more variables. The aim of this work is to analyze the passage to the singular limit when the memory kernel collapses into a Dirac mass. In particular, we focus on the reaction-diffusion equation with memory, and we discuss the convergence of solutions on finite time-intervals. When enough dissipativity is present, we also establish convergence results of the global and the exponential attractors. Nonetheless, the techniques here devised are quite general, and suitable to be applied to a large variety of models.
Indiana University Mathematics Journal
2006
text
pdf
10.1512/iumj.2006.55.2661
10.1512/iumj.2006.55.2661
en
Indiana Univ. Math. J. 55 (2006) 169 - 216
state-of-the-art mathematics
http://iumj.org/access/