Global Existence in Time and Decay Property of Solutions of Boundary Value Problems for Semilinear Hyperbolic Equations of Second Order in the Interior Domain | Zendy

Akisato Kubo | Zendy

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Global Existence in Time and Decay Property of Solutions of Boundary Value Problems for Semilinear Hyperbolic Equations of Second Order in the Interior Domain

Author(s) -

Akisato Kubo

Publication year - 1998

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195144829

Subject(s) - mathematics , order (exchange) , domain (mathematical analysis) , operator (biology) , boundary value problem , elliptic operator , hyperbolic partial differential equation , mathematical analysis , mathematical physics , combinatorics , pure mathematics , partial differential equation , chemistry , biochemistry , finance , repressor , transcription factor , economics , gene

(0.3) P * [ ] = 9 ? Z 9, (a „(*,*) 9,)+A( t ,* ;u ,A*)[w] «,/=! (0.4) A ( f , * ; u , / l K ) [ ] = S aaB(t.x\u.Au)A*A, 9t"a~, ^~ir~> i — 1, '",n, Au (dtu, d\u, , 9Mti), a= (a0, ai, • • , a«), /J— OSo, A, , ^8W) are multi-indices, and Aw= (dfdT'"dnua— (a0, ai, • • , aj). We next make following assumptions on PM. n (A-I) 2 d l ( a l j ( t , x}d}) is an elliptic operator satisfying for all r] ^W 1 u=i (0.5) Zfl, /)7,)?^CoS7??(Co>0)I u'=i »=i fliy(t, ^) =ay< (t, x) (i, ; = ! ,—, n) for all (t, *) e [0, oo) x Q,

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