The Role of Critical Exponents in Blowup Theorems

Critical Exponent for Semilinear Wave Equations with Space-Dependent Potential

“…The number p w ðNÞ is refered as Strauss critical exponent. See also the survey papers of Levine [17] and Deng and Levine [16].…”

Nonexistence results for the Cauchy problem of some systems of hyperbolic equations

“…In statement (ii) the subcritical case was proved by John [4] when N = 3 and by Glassey [3] for N = 2, 3; the critical case was settled by Schaeffer [9] for N = 2, 3; and the supercritical case was proved by Glassey [3] when N = 2 and by John [4] for N = 3. A valuable review of results on blowing up solutions to evolution equations is presented in [6].…”

Deciphering singularities by discrete methods

“…Thus, x has no real singularities if |xn| < 1 . This situation is typical of many differential problems for which global existence for t > 0 is only guaranteed if the size of the initial datum is below a certain threshold [17]. We use the classical RungeKutta method [4] for the discretization of (3.1).…”

“…This problem and its generalizations have received considerable attention in the literature [17,21]. In this section, we propose to trace numerically the motion of the singularities in the complex plane as the parameter a varies.…”