一类半线性波动方程的适定性

Abstract

Abstract:

We consider the global small data solutions and blowup to the Cauchy problem for a semilinear wave equation with time-dependent damping and mass term as well as power nonlinearity. On one hand, if the power of the nonlinearity $p >p_F(N)=1+ \frac 2N$, it is proved that solutions with small initial data exist for all time in exponentially weighted energy spaces. On the other hand, if the power satisfies <p\leq p_F(\alpha, n)=1+\frac{2(1+\alpha)}{N(1+\alpha)-2\alpha}~(0<\alpha<1)$, for some special chosen parameters it is shown that solutions must blow up in finite time provided that the initial data satisfy some integral sign conditions.

Key words: Semilinear wave equation, Global solution, Blow up, Fujita exponent

CLC Number:

O175.27

Changwang Xiao,Fei Guo. Global Existence and Blowup Phenomena for a Semilinear Wave Equation with Time-Dependent Damping and Mass in Exponentially Weighted Spaces[J].Acta mathematica scientia,Series A, 2020, 40(6): 1568-1589.

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References 25

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Global Existence and Blowup Phenomena for a Semilinear Wave Equation with Time-Dependent Damping and Mass in Exponentially Weighted Spaces

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