Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Remarks on a paper by W. A. Day on a maximum principle under nonlocal boundary conditions


Author: Bernhard Kawohl
Journal: Quart. Appl. Math. 44 (1987), 751-752
MSC: Primary 35B50; Secondary 35K20
DOI: https://doi.org/10.1090/qam/872825
MathSciNet review: 872825
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Abstract: In a recent paper W. A. Day proved a decay property for solutions to a linear parabolic equation with nonlocal boundary conditions. Such boundary conditions arise in thermoelasticity. We extend his result (a) from one to arbitrary space dimensions, (b) from linear to nonlinear parabolic equations, and (c) from differential equations to differential inequalities. Our tool is the classical maximum principle.


References [Enhancements On Off] (What's this?)

  • [1] Peter Bader, On a quasilinear elliptic boundary value problem of nonlocal type with an application in combustion theory, Z. Angew. Math. Phys. 35 (1984), no. 6, 771–779 (English, with German summary). MR 777860, https://doi.org/10.1007/BF00945442
  • [2] W. A. Day, A decreasing property of solutions of parabolic equations with applications to thermoelasticity, Quart. Appl. Math. 40, 468-475 (1983)
  • [3] B. P. Paneyakh, Some nonlocal boundary value problems for linear differential operators, Mat. Zametki 35 (1984), no. 3, 425–434 (Russian). MR 741809
  • [4] Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0219861

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Additional Information

DOI: https://doi.org/10.1090/qam/872825
Article copyright: © Copyright 1987 American Mathematical Society


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