Existence of asymptotic speed of solutions to birth and spread type nonlinear partial differential equations
arXiv:1808.063129 citationsh-index: 52
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Provides a theoretical foundation for propagation speed in nonlinear PDEs, relevant to mathematical biology and physics.
Proved existence of asymptotic speed for a broad class of nonlinear degenerate parabolic PDEs, with explicit examples and numerical validation.
In this paper, we prove the existence of asymptotic speed of solutions to fully nonlinear, possibly degenerate parabolic partial differential equations in a general setting. We then give some explicit examples of equations in this setting and study further properties of the asymptotic speed for each equation. Some numerical results concerning the asymptotic speed are presented.