We consider some initial-boundary value problems for a class of nonlinear parabolic equations of the fourth order, whose 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). Under appropriate assumptions on the data, a criterion which ensures that u cannot exist for all time is given, and an upper bound for t* is derived. Some extensions for a class of nonlinear fourth order parabolic systems are indicated.
|Titolo:||Behaviour in time of solutions to a class of fourth order evolution equations.|
|Data di pubblicazione:||2015|
|Tipologia:||1.1 Articolo in rivista|