Global Nonexistence for Nonlinear Kirchhoff Systems

By G. Autuori, Patrizia Pucci, M. Salvatori. 2010

148 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bc8e857cf7a1eaed2ef135bd720b84aa2c2e4a19

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

A Blow-Up Result in a Nonlinear Wave Equation with Delay (2016, background): “[3] investigated the global nonexistence for nonlinear Kirchhoff system.”
Multiplicity results for the non-homogeneous fractional p-Kirchhoff equations with concave–convex nonlinearities (2015, background): “6) has received a lot of attention, and some interesting results can be found in, for example, [32] for the non-degenerate case and [33] for the degenerate case, also in [34] for the time case.”
On double phase Kirchhoff problems with singular nonlinearity (2021, methodology): “In the extensive literature on degenerate and nondegenerate Kirchhoff problems, we refer, for example, to the works of Arora-Giacomoni-Mukherjee-Sreenadh [1, 2], Autuori-Pucci-Salvatori [5], D’Ancona-Spagnolo [14], Figueiredo [19], Fiscella [21], Fiscella-Valdinoci [24], Mingqi-Rădulescu-Zhang [38],”
Wave Equation with p(x,t) - Laplacian and Damping Term: Existence and Blow-up (2011, background): “The hyperbolic equations with nonstandard growth conditions, to the best of our knowledge, were considered only in papers [14, 15, 22, 34].”
A multiplicity result for a fractional Kirchhoff equation in ℝN with a general nonlinearity (2016, result): “For more recent results concerning Kirchhoff-type equations we refer to [1, 2, 5, 7, 16, 22, 25, 30].”
On a fractional degenerate Kirchhoff-type problem (2017, methodology): “We cite, amid the wide literature on the subject, the works [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 18, 20] where Kirchhoff-type problems (also in their stationary versions) were studied by exploiting different methods and new technical approaches.”
On the strongly damped wave equation with nonlinear damping and source terms (2009, background): “Ono [19] showed that the solution of (1.1) blow up in finite time if E(0) 0, which automatically implies u0 ∈ N+. Ohta [18] improves this result by allowing E(0) d and u0 ∈ N+. Gazzola and Squassina [8] extended this result to the case when µ 6= 0 and E(0) ≤ d.”
On solutions of space–fractional diffusion equations by means of potential wells (2016, methodology): “Concerning the analysis of blow up of solutions, we refer to the papers [1], [25] and [26], where several different methods are applied.”