Global stability of solutions to two-dimension and one-dimension systems of semilinear wave equations

Zha, Dongbing

doi:10.1016/j.jfa.2021.109219

Cited by 10 publications

(3 citation statements)

References 28 publications

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“…Of course, some special structure of the nonlinear terms such as "null condition" guarantees the global-in-time existence. See Nakamura [22], Luli, Yang and Yu [21], Zha [34,35] for examples in this direction. But we are interested in the optimality of the general theory.…”

Section: Comparison With the General Theorymentioning

confidence: 99%

The lifespan of classical solutions of semilinear wave equations with spatial weights and compactly supported data in one space dimension

Kitamura

Morisawa

Takamura

2022

Journal of Differential Equations

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Section: Comparison With the General Theorymentioning

confidence: 99%

The lifespan of classical solutions of semilinear wave equations with spatial weights and compactly supported data in one space dimension

Kitamura

Morisawa

Takamura

2022

Journal of Differential Equations

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“…Of course, some special structure of the nonlinear terms such as "null condition" guarantees the global-in-time existence. See Zha [13,14] for example in this direction. But we are interested in the optimality of the general theory.…”

Section: Introductionmentioning

confidence: 99%

The combined effect in one space dimension beyond the general theory for nonlinear wave equations

Morisawa¹,

Sasaki²,

Takamura³

2022

Preprint

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In this paper, we show the so-called "combined effect" of two different kinds of nonlinear terms for semilinear wave equations in one space dimension. Such a special phenomenon appears only in the case that the total integral of the initial speed is zero. It is remarkable that, including the combined effect case, our results on the lifespan estimates are partially better than those of the general theory for nonlinear wave equations.

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“…Of course, some special structure of the nonlinear terms such as "null condition" guarantees the global-in-time existence. See Nakamura [13], Luli, Yang and Yu [12], Zha [15,16] for examples in this direction. But we are interested in the optimality of the general theory.…”

mentioning

confidence: 99%

The combined effect in one space dimension beyond the general theory for nonlinear wave equations

Morisawa¹,

Sasaki²,

Takamura³

2023

CPAA

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In this paper, we show the so-called "combined effect" of two different kinds of nonlinear terms for semilinear wave equations in one space dimension. This effect means that the lifespan, the maximal existence time, of the classical solution is shorter than the minimum of ones for each term. Such a special phenomenon has been observed in all space dimensions except for one space dimension. We succeed to pick up the combined effect in one space dimension by classifying the lifespan estimates according to whether the total integral of the initial speed is zero, or not, and it is obtained only in the first case. It is also remarkable that, including the combined effect, our results on the lifespan estimates are partially better than those of the general theory for nonlinear wave equations which was considered completed about 30 years ago.1. Introduction. We consider the initial value problems;where p, q > 1, A, B ≥ 0, f and g are given smooth functions of compact support and a parameter ε > 0 is "small enough". We are interested in the lifespan T (ε),

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Global stability of solutions to two-dimension and one-dimension systems of semilinear wave equations

Cited by 10 publications

References 28 publications

The lifespan of classical solutions of semilinear wave equations with spatial weights and compactly supported data in one space dimension

The lifespan of classical solutions of semilinear wave equations with spatial weights and compactly supported data in one space dimension

The combined effect in one space dimension beyond the general theory for nonlinear wave equations

The combined effect in one space dimension beyond the general theory for nonlinear wave equations

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