Time—periodic weak solutions

Eliana Henriques de Brito

International Journal of Mathematics and Mathematical Sciences, 1990, vol. 13, 1-6

Abstract:

In continuing from previous papers, where we studied the existence and uniqueness of the global solution and its asymptotic behavior as time t goes to infinity, we now search for a time-periodic weak solution u ( t ) for the equation whose weak formulation in a Hilbert space H is d d t ( u ′ , v ) + δ ( u ′ , v ) + α b ( u , v ) + β a ( u , v ) + ( G ( u ) , v ) = ( h , v ) where: ′ = d / d t ; ( ′ ) is the inner product in H ; b ( u , v ) , a ( u , v ) are given forms on subspaces U ⊂ W , respectively, of H ; δ > 0 , α ≥ 0 , β ≥ 0 are constants and α + β > 0 ; G is the Gateaux derivative of a convex functional J : V ⊂ H → [ 0 , ∞ ) for V = U , when α > 0 and V = W when α = 0 , hence β > 0 ; v is a test function in V ; h is a given function of t with values in H.

Application is given to nonlinear initial-boundary value problems in a bounded domain of R n .

Date: 1990
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:464936

DOI: 10.1155/S0161171290000199

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