The authors obtain sharp lifespan estimates for 1D wave equations with space-derivative semilinear terms and give a simple blow-up proof via iteration and slicing that reduces part of the problem to the Li-Zhou ODE inequality.
John,Blow-up of solutions of nonlinear wave equations in three space dimensions, Manuscripta Math.,28(1979), no
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Lifespan estimate for one dimensional wave equation with semilinear terms of spatial derivative
The authors obtain sharp lifespan estimates for 1D wave equations with space-derivative semilinear terms and give a simple blow-up proof via iteration and slicing that reduces part of the problem to the Li-Zhou ODE inequality.