Joseph Cima, William Derrick, Leonid Kalachev, "Watersheds for Solutions of Nonlinear Parabolic Equations," WSEAS Transactions on Mathematics, vol. 17, pp. 170-177, 2018, DOI:
Joseph Cima, William Derrick, Leonid Kalachev. Watersheds for Solutions of Nonlinear Parabolic Equations.
WSEAS Transactions on Mathematics. 2018;17:170-177.
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 17, 2018
Watersheds for Solutions of Nonlinear Parabolic Equations
Authors: , ,
Abstract: In this paper we describe a technique that we have used in a number of publications to find the “water-shed” under which the initial condition of a positive solution of a nonlinear reaction-diffusion equation must lie, so that this solution does not develop into a traveling wave, but decays into a trivial solution. The watershed consists of the positive solution of the steady-state problem together with positive pieces of nodal solutions ( with identical boundary conditions). We prove in this paper that our method for finding watersheds works in R^k, k ≥ 1, for increasing functions f(z)/z. In addition, we weaken the condition that f(z)/z be increasing, and show that the method also works in R1 when f(z)/z is bounded. The decay rate is exponential.
Pages: 170-177 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 17, 2018, Art. #22 DOI: *As the DOI is a unique identifier, it is already available in the pdf version.
**The DOI link will be activated in the first midst of January 2026.
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