93 citations · 491 across the 27 of their papers we have counts for
4 papers · 2 filters
Improved Kato's lemma on ordinary differential inequality and its application to semilinear wave equations
Hiroyuki Takamura
We are interested in the upper bound of the lifespan of solutions of semilinear wave equations from above. For the sub-critical case in high dimensions, it has been believed that t…
Blow-Up of Positive Solutions to Wave Equations in High Space Dimensions
Hiroyuki Takamura, Mohammad Rammaha, Hiroshi Uesaka +1
This paper is concerned with the Cauchy problem for the semilinear wave equation: $u_{tt}-Δu=F(u) \ \mbox{in} \ R^n\times[0, \infty)$, where the space dimension , $F(u)=|u…
Global existence for semilinear wave equations with the critical blow-up term in high dimensions
Hiroyuki Takamura, Kyouhei Wakasa
We are interested in almost global existence cases in the general theory for nonlinear wave equations, which are caused by critical exponents of nonlinear terms. Such situations ca…
Almost global solutions of semilinear wave equations with the critical exponent in high dimensions
Hiroyuki Takamura, Kyouhei Wakasa
We are interested in the "almost" global-in-time existence of classical solutions in the general theory for nonlinear wave equations. All the three such cases are known to be sharp…