The fundamental analysis method for the blow-up of wave equations in first quadrant

作者：Han Wei^*

来源：Journal of Mathematical Analysis and Applications, 2017, 456(1): 525-542.

DOI：10.1080/0023131.2017.07.004

• Wave equations
• Blow up
• Life-span
• Initial-boundary value problem

This paper is devoted to prove the sharpness on the lower bound of the life-span of classical solutions to the initial-boundary value problem for one dimensional general quasilinear wave equations in the general case obtained in [10]. What's more, the originality of the paper is the fundamental analysis method of the blow-up and lifespan property, that is to say, instead of differential inequality and the pure mathematical analysis, this is the first attempt to this direction. The highlight of the paper is that we will use the most fundamental D'Alembert's formula of the solutions of wave equation, and the corresponding actual physical meaning, by means of the scaling argument, dilation translation, translation transformation, rotation transformation, we connect our problem with a Goursat problem, and then we can intuitively obtain our blow-up and lifespan result for the problem, this is a new idea in the paper.

• 出版日期2017-12-1
• 单位中北大学