Positivity for elliptic and parabolic systems
Copyright policy )Positivity for elliptic and parabolic systems
SynopsisThe positivity of solutions of initial-boundary value problems for weakly-coupled semilinear parabolic or elliptic systems of equations is studied. Conditions on the coupling terms are described which ensure that the solutions of the parabolic systems remain positive whenever the initial conditions are positive. For elliptic systems involving a parameter, conditions on the coupling terms are described which imply that solution branches which contain a positive solution, in fact, contain only positive solutions. Applications of these theorems to certain reaction-diffusion equations arising in the modelling of biological phenomena are given.
- DePaul University United States
initial-boundary value problems, positivity of solutions, Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, Population dynamics (general), reaction-diffusion equations, semilinear parabolic or elliptic systems, Nonlinear elliptic equations, coupling terms
initial-boundary value problems, positivity of solutions, Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, Population dynamics (general), reaction-diffusion equations, semilinear parabolic or elliptic systems, Nonlinear elliptic equations, coupling terms
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