An elementary proof of the blow-up for semilinear wave equation in high space dimensions

By H. Jiao, Zhengfang Zhou. 2003

56 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8c91d463a02ccc59c55a1763d752048cd944f4eb

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In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Semi‐linear wave models with power non‐linearity and scale‐invariant time‐dependent mass and dissipation (2017, background): “If 1 < p ≤ p0(n) and n ≥ 1, then energy solutions for the semi-linear Cauchy problem for the free wave equation blow-up for a suitable choice of small initial data, see [10], [13], [14], [20], [21], [27].”
A competition between Fujita and Strauss type exponents for blow-up of semi-linear wave equations with scale-invariant damping and mass (2019, methodology): “), the critical exponent is the so-called Strauss exponent p 0(n), which is deﬁned as the positive root of the quadratic equation (n−1)p2 −(n+1)p−2 = 0. In particular, we refer to the classical works [16, 17, 8, 27, 26, 15, 39, 41] and references therein for blow-up results when 1 <p≤ p 0(n). In ”
A shift in the Strauss exponent for semilinear wave equations with a not effective damping (2015, background): “r the existence of global (in time) small data solutions is p0(n). More precisely, if 1 <p≤ p0(n), then solutions to (2) blow-up in ﬁnite time for a suitable choice of initial data (see [9], [13], [14], [20], [21], [24]), whereas for p∈ (p0(n),(n+ 3)/(n− 1)] a unique global (in time) small data s”
Finite time blow up for critical wave equations in high dimensions (2004, methodology): “Here we remark that (2.7) have been proven in [Si] and [ JZ ] by different method.”
Life-Span of Solutions to Critical Semilinear Wave Equations (2011, background): “[15] [21] and [18]), this is the famous Strauss’ conjecture, we only give a brief summary here and refer the reader to [4, 6, 8, 9, 11, 17, 20].”
Nonexistence of global solutions for the semilinear Moore – Gibson – Thompson equation in the conservative case (2019, background): “According to [17, 21, 39, 12, 13, 38, 37, 49, 27, 11, 42, 16, 45, 50, 22] the so – called Strauss exponent pStr(n) is the critical exponent of (1.”