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Growth of solutions of weakly coupled parabolic systems and Laplace's equation

Part of: Higher-dimensional theory Elliptic equations and systems Partial differential equations Parabolic equations and systems

Published online by Cambridge University Press:  09 April 2009

N. A. Watson
N. A. Watson
Affiliation:
Department of Mathematics, University of Canterbury, Christchurch, New Zealand
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Abstract

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Let ui(x, t) be the ith component of a nonnegative solution of a weakly coupled system of second-order, linear, parabolic partial differential equations, for x ∈ Rn and 0 < t < T. We obtain lower estimates, near t = 0, for the Lebesgue measure of the set of x for which exceeds 1. Related results for Poisson integrals on a half-space are also described, some applications are given, and interesting comparisons emerge.

MSC classification

Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 31B05: Harmonic, subharmonic, superharmonic functions 31B25: Boundary behavior 35B30: Dependence of solutions on initial and boundary data, parameters 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation 35K45: Initial value problems for second-order parabolic systems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 41 , Issue 3 , December 1986 , pp. 391 - 403
Copyright
Copyright © Australian Mathematical Society 1986

References

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