Weakly coupled system of semilinear wave equations with distinct scale-invariant terms in the linear part

Abstract

In this work we determine the critical exponent for a weakly coupled system of semilinear wave equations with distinct scale-invariant lower order terms, when these terms make both equations in some sense parabolic-like. For the blow-up result the test functions method is applied, while for the global existence (in time) results we use L2-L2 estimates with additional L1 regularity.

19 pages

References in corpus (2)

• A note on the blowup of scale invariant damping wave equation with sub-Strauss exponent
• A note on a conjecture for the critical curve of a weakly coupled system of semilinear wave equations with scale-invariant lower order terms

Cited by in corpus (7)

• The semilinear Euler-Poisson-Darboux equation: a case of wave with critical dissipation
• Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity
• A note on a conjecture for the critical curve of a weakly coupled system of semilinear wave equations with scale-invariant lower order terms
• A blow-up result for a semilinear wave equation with scale-invariant damping and mass and nonlinearity of derivative type
• Blow-up results for semilinear damped wave equations in Einstein-de Sitter spacetime
• Sharp lifespan estimates for the weakly coupled system of semilinear damped wave equations in the critical case
• Integral representation formulae for the solution of a wave equation with time-dependent damping and mass in the scale-invariant case