Document Type

Article - postprint

Department

Mathematics (HMC)

Publication Date

11-1980

Abstract

In this paper, we study the existence of weak solutions of the problem

□u + ∇G(u) = f(t,x) ; (t,x) є Ω ≡ (0,π)x(0,π)

u(t,x) = 0 ; (t,x) є ∂Ω

where □ is the wave operator ∂2/∂t2 - ∂2/∂x2, G: Rn→R is a function of class C2 such that ∇G(0) = 0 and f:Ώ→R^n is a continuous function having first derivative with respect to t in (L2,(Ω))n and satisfying

f(0,x) = f(π,x) = 0

for all x є [0,π].

Comments

Author's post-print manuscript available for download.

For the publisher's PDF, please visit http://dx.doi.org/10.1016/0362-546X(80)90024-3.

Rights Information

© 1980 Elsevier

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