Department of Mathematics and Education
Universidad a Distancia de Madrid
28400 Madrid, Spain
email: joseluis.diaz.p@udima.es
Jose Luis Diaz Palencia
Abstract:
This analysis explores the oscillatory behavior of
traveling wave solutions for a higher-order p-Laplacian operator with
a superlinear reaction term. The study employs an energy-based approach,
incorporating generalized Sobolev spaces to examine relevant properties
of the solutions, including oscillations, diffusive mollification,
and compact support. Based on this energy framework, the regularity of
the involved operator is established.
The problem is then reformulated using a traveling wave approach,
revealing the oscillatory nature of solutions near the null solution.
Numerical simulations are conducted for each wave speed to validate the
analytical results, yielding the corresponding traveling profiles.
Notably, one of the most significant findings is the attraction towards
the null critical point, which helps prevent blow-up formation.
Finally, the study delves into the equation's scale-invariant properties,
leading to the derivation of self-similar solutions.
Submitted June 18, 2024. Published November 7, 2024.
Math Subject Classifications: 35K92, 35K91, 35K55.
Key Words: Higher order p-Laplacian operator; travelling waves; homotopy; superlinear reaction.
DOI: 10.58997/ejde.2024.68
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José Luis Díaz Palencia Department of Mathematics and Education Universidad a Distancia de Madrid 28400 Madrid, Spain email: joseluis.diaz.p@udima.es |
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