@article {31614,
title = {Elliptic-like regularization of semilinear evolution equations},
journal = {Journal of Mathematical Anallysis and Applications},
volume = {396},
year = {2012},
pages = {759{\textendash}771},
abstract = {Consider in a real Hilbert space the Cauchy problem (P0): u'(t)+Au(t)+Bu(t) = f (t), 0 <= t <= T ; u(0) = u_0, where -A is the generator of a C_0-semigroup of linear contractions and B is a smooth nonlinear operator. We associate with (P_0) the following problem: (Pε): -εu''(t) + u'(t) + Au(t) + Bu(t) = f (t), 0 <= t <= T ; u(0) = u_0, u(T ) = u_1, where ε > 0 is a small parameter. Existence, uniqueness and higher regularity for both (P0) and (Pε) are investigated and an asymptotic expansion for the solution of problem (Pε) is established, showing the presence of a boundary layer near t = T .
},
doi = {10.1016/j.jmaa.2012.07.020},
url = {http://www.sciencedirect.com/science/article/pii/S0022247X12005835},
author = {Ahsan, Muhammad and Morosanu, Gheorghe}
}