Open AccessBlow-up phenomena for nonlinear pseudo-parabolic equations with gradient term
Author(s) -
Monica Marras,
Stella VernierPiro,
Giuseppe Viglialoro
Publication year - 2017
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2017096
Subject(s) - nabla symbol , omega , domain (mathematical analysis) , bounded function , boundary (topology) , combinatorics , physics , interval (graph theory) , parabolic partial differential equation , lambda , constant (computer programming) , function (biology) , mathematical analysis , nonlinear system , mathematics , quantum mechanics , evolutionary biology , computer science , biology , programming language
This paper is concerned with the pseudo-parabolic problem \ud\ud{ u(t) - lambda Delta u(t) =k(t)div(g(vertical bar del u vertical bar(2))del u) + f (t, u, vertical bar del u vertical bar) in Omega x (0,t*), \ud\udu =0 on partial derivative Omega x (0, t*), \ud\udu(x, 0) =u(0)(x) in Omega, \ud\udwhere Omega is a bounded domain in R-n, n >= 2, with smooth boundary partial derivative Omega, k is a positive constant or in general positive derivable function of t. The solution u(x, t) may or may not blow up in finite time. Under suitable conditions on data, a lower bound for t* is derived, where [0,t*) is the time interval of existence of u(x, t). We indicate how some of our results can be extended to a class of nonlinear pseudo-parabolic system