Abstract
In the present paper, the local existence of classical solutions to the periodic boundary problem and the Cauchy problem of a quasilinear evolution equation utt-Δut=∑i=1n∂∂xiσi(uxi)are studied under the assumptions that do not require the monotonicity of σi(s) (i = 1, …, n). The nonexistence of global solutions to the initial-boundary value problem of the equation is also discussed, a blowup theorem is proved and a concrete example is given.
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