Global solutions and finite time blow up for damped semilinear wave equations ? ? The first author w

By Filippo Gazzola, Marco Squassina. 2006

272 citations recorded by the source corpus.

A class of damped wave equations with superlinear source term is considered. It is shown that every global solution is uniformly bounded in the natural phase space. Global existence of solutions with initial data in the potential well is obtained. Finally, not only finite time blow up for solutions starting in the unstable set is proved, but also high energy initial data for which the solution blows up are constructed.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fe2eb3d853bc92c2dd96bd6a656d57d557aef49f

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In Computational Theory and Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

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.”
Local existence and exponential growth for a semilinear damped wave equation with dynamic boundary conditions (2008, methodology): “Unfortunately, the presence of the nonlinear boundary conditions excludes us to use the spatial basis of eigenfunctions of −∆ in H(1) Γ0 (Ω) as done in [14]”
Initial boundary value problem for semilinear hyperbolic equations and parabolic equations with critical initial data (2010, background): “Because it is not possible to cite all of the more than one hundred papers on the subject, we refer the reader to [4]–[6], [8]–[10], [16]–[22] and the references therein.”
Energy decay estimates and infinite blow‐up phenomena for a strongly damped semilinear wave equation with logarithmic nonlinear source (2018, background): “Let d(δ) be defined by (11), and λ1 be the first eigenvalue of problem (12).”