TY - JOUR

T1 - Asymptotic and other estimates for a semilinear elliptic equation in a cylinder

AU - Flavin, J. N.

AU - Knops, R. J.

AU - Payne, L. E.

PY - 1992/11

Y1 - 1992/11

N2 - We consider a semilinear elliptic equation in a cylinder of variable cross-section subject to zero conditions on the lateral boundaries. A second-order differential inequality is obtained for an L2p cross-sectional measure of the solution, where p is a positive integer.It is used to obtain an upper bound for the measure in terms of data, supposed specified on the plane ends of the cylinder (finite cylinder). A semi-infinite cylinder is then considered-the principal concern of the paper-and propositions are proved therefor;a global solution, when it exists, must decay at least exponentially in both cross-sectional and energy measures. These results, obtained without assuming that the solution tends to zero at large distances, depend crucially upon a lemma derived from the basic second-order differential inequality. © 1992 Oxford University Press.

AB - We consider a semilinear elliptic equation in a cylinder of variable cross-section subject to zero conditions on the lateral boundaries. A second-order differential inequality is obtained for an L2p cross-sectional measure of the solution, where p is a positive integer.It is used to obtain an upper bound for the measure in terms of data, supposed specified on the plane ends of the cylinder (finite cylinder). A semi-infinite cylinder is then considered-the principal concern of the paper-and propositions are proved therefor;a global solution, when it exists, must decay at least exponentially in both cross-sectional and energy measures. These results, obtained without assuming that the solution tends to zero at large distances, depend crucially upon a lemma derived from the basic second-order differential inequality. © 1992 Oxford University Press.

UR - http://www.scopus.com/inward/record.url?scp=5544291034&partnerID=8YFLogxK

U2 - 10.1093/qjmam/45.4.617

DO - 10.1093/qjmam/45.4.617

M3 - Article

VL - 45

SP - 617

EP - 627

JO - Quarterly Journal of Mechanics and Applied Mathematics

JF - Quarterly Journal of Mechanics and Applied Mathematics

SN - 0033-5614

IS - 4

ER -