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.

Behaviour in time of solutions to a class of fourth order evolution equations

PIRO, STELLA
Secondo
2016

Abstract

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.
Semilinear fourth order parabolic equations; Fourth order parabolic systems; Blow-up
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/135879
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