Elliptic-like regularization of semilinear evolution equations

TitleElliptic-like regularization of semilinear evolution equations
Publication TypeJournal Article
AuthorsAhsan, Muhammad, and Gheorghe Morosanu
Journal titleJournal of Mathematical Anallysis and Applications
Year2012
Pages759–771
Volume396
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 .

LanguageEnglish
DOI10.1016/j.jmaa.2012.07.020
Publisher linkhttp://www.sciencedirect.com/science/article/pii/S0022247X12005835
Unit: 
Department of Mathematics and its Applications
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