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Interactions of semilinear progressing waves in two or more space dimensions
Inverse Problems and Imaging ( IF 1.3 ) Pub Date : 2020-08-28 , DOI: 10.3934/ipi.2020055
Antônio Sá Barreto ,

We analyze the behavior of the singularities of solutions of semilinear wave equations after the interaction of three transversal conormal waves. Our results hold for space dimensions two and higher, and for arbitrary $ {{C}^{\infty }} $ nonlinearity. The case of two space dimensions in which the nonlinearity is a polynomial was studied by the author and Yiran Wang. We also indicate possible applications to inverse problems.

中文翻译:

半线性行波在两个或多个空间维度上的相互作用

我们分析了三个横向同正态波的相互作用之后半线性波动方程解的奇异性的行为。我们的结果适用于两个或两个以上维度的空间,以及任意的$ {{C} ^ {\ infty}} $非线性。作者和王一然研究了二维空间中非线性为多项式的情况。我们还指出了反问题的可能应用。
更新日期:2020-11-06
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