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| THE BLOWUP OF RADIALLY SYMMETRIC SOLUTIONS FOR2-D QUASILINEAR WAVE EQUATIONS WITH CUBIC NONLINEARITY |
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Citation： |
YIN Huicheng,ZHENG Qin.THE BLOWUP OF RADIALLY SYMMETRIC SOLUTIONS FOR2-D QUASILINEAR WAVE EQUATIONS WITH CUBIC NONLINEARITY[J].Chinese Annals of Mathematics B,1999,20(4):455~472 |
| Page view： 1010
Net amount： 730 |
Authors： |
YIN Huicheng; ZHENG Qin |
Foundation： |
Project supported by the Tianyuan Foundation of Mathematics of
China and Laboratary of Mathematics for Nonlinear Sciences at
Fudan University. |
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| Abstract： |
For a special class of quasilinear wave equations with small initial data
which satisfy the nondegenerate assumption, the authors
prove that the radially symmetric solution develops singularities in the
second order derivatives in finite time while the first order derivatives
and the solution itself remain continuous and small. More precisely, it turns out that
this solution is a ``geometric blowup solution of cusp type'', according to
the terminology posed by S. Alinhac$^{[2]}$. |
Keywords： |
Lifespan, Geometric blowup,
Nash-M$\ddot {\text{o}}$ser iteration |
Classification： |
35L40 |
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