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Modified KdV equation with a source term in a bounded domain
Author(s) -
Larkin N. A.
Publication year - 2006
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.704
Subject(s) - korteweg–de vries equation , mathematics , uniqueness , bounded function , term (time) , domain (mathematical analysis) , sign (mathematics) , exponential function , mathematical analysis , mathematical physics , pure mathematics , physics , quantum mechanics , nonlinear system
A mixed problem for the modified KdV equation in Q = (0,1) × (0,∞)$$u_t + b(t)uu_{x}+ a(t)u_{xxx}+ d(t)u= f(x,t) $$where a ( t )>0, is considered. No restriction on the sign of d ( t ) is imposed. We prove the existence and uniqueness of strong and weak global solutions as well as the exponential decay of solutions as t →+∞. Copyright © 2006 John Wiley & Sons, Ltd.
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