dc.contributor.author | Iagar, Razvan Gabriel | |
dc.contributor.author | Muñoz Montalvo, Ana Isabel | |
dc.contributor.author | Sánchez, Ariel | |
dc.date.accessioned | 2023-11-30T11:33:02Z | |
dc.date.available | 2023-11-30T11:33:02Z | |
dc.date.issued | 2023-11 | |
dc.identifier.citation | Iagar, R. G., Munoz, A. I., & Sanchez, A. (2023). Qualitative properties of solutions to a reaction-diffusion equation with weighted strong reaction. Electronic Journal of Differential Equations, 2023(01-??), No. 72, 1–21. https://doi.org/10.58997/ejde.2023.72 | en |
dc.identifier.issn | 1072-6691 | |
dc.identifier.uri | https://hdl.handle.net/10115/26769 | |
dc.description.abstract | We study the existence and qualitative properties of solutions to the Cauchy problem associated to the quasilinear reaction-diffusion equation
∂tu = ∆u^m + (1 + |x|)^σ u^p,
posed for (x, t) ∈ R^N × (0, ∞), where m > 1, p ∈ (0, 1) and σ > 0. Initial data
are taken to be bounded, non-negative and compactly supported. In the range
when m + p ≥ 2, we prove existence of local solutions with a finite speed of
propagation of their supports for compactly supported initial conditions. We
also show in this case that, for a given compactly supported initial condition,
there exist infinitely many solutions to the Cauchy problem, by prescribing the
evolution of their interface. In the complementary range m + p < 2, we obtain
new Aronson-Bénilan estimates satisfied by solutions to the Cauchy problem,
which are of independent interest as a priori bounds for the solutions. We
apply these estimates to establish infinite speed of propagation of the supports
of solutions if m + p < 2, that is, u(x, t) > 0 for any x ∈ R^N , t > 0, even in
the case when the initial condition u0 is compactly supported. | en |
dc.language.iso | eng | es |
dc.rights | Atribución 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | * |
dc.subject | Reaction-diffusion equations; weighted reaction; strong reaction; Aronson-Bénilan estimates. | en |
dc.title | Qualitative properties of solutions to a reaction-diffusion equation with weighted strong reaction | es |
dc.type | info:eu-repo/semantics/article | es |
dc.identifier.doi | 10.58997/ejde.2023.72 | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |