Nonlinear Wave Equations

1. Introduction and Overview
Tatsien Li, Yi Zhou

2. Linear Wave Equations
Tatsien Li, Yi Zhou

3. Sobolev Type Inequalities with Decay Factor
Tatsien Li, Yi Zhou

4. Estimates on Solutions to the Linear Wave Equations
Tatsien Li, Yi Zhou

5. Some Estimates on Product Functions and Composite Functions
Tatsien Li, Yi Zhou

6. Cauchy Problem of the Second-Order Linear Hyperbolic Equations
Tatsien Li, Yi Zhou

7. Reduction of Nonlinear Wave Equations to a Second-Order Quasi-linear Hyperbolic System
Tatsien Li, Yi Zhou

8. Cauchy Problem of One-Dimensional Nonlinear Wave Equations
Tatsien Li, Yi Zhou

9. Cauchy Problem of




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n
(
≥
3
)

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-Dimensional Nonlinear Wave Equations
Tatsien Li, Yi Zhou

10. Cauchy Problem of Two-Dimensional Nonlinear Wave Equations
Tatsien Li, Yi Zhou

11. Cauchy Problem of Four-Dimensional Nonlinear Wave Equations
Tatsien Li, Yi Zhou

12. Null Condition and Global Classical Solutions to the Cauchy Problem of Nonlinear Wave Equations
Tatsien Li, Yi Zhou

13. Sharpness of Lower Bound Estimates on the Life-Span of Classical Solutions to the Cauchy Problem—The Case that the Nonlinear Term




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F
=
F
(
D
u
,

D
x

D
u
)

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on the Right-Hand Side Does not Depend on u Explicitly
Tatsien Li, Yi Zhou

14. Sharpness of Lower Bound Estimates on the Life-Span of Classical Solutions to the Cauchy Problem—The Case that the Nonlinear Term




]]>

F
=
F
(
u
,
D
u
,

D
x

D
u
)

]]>
on the Right-Hand Side Depends on u Explicitly
Tatsien Li, Yi Zhou

15. Applications and Developments
Tatsien Li, Yi Zhou

Nyckelord: Mathematics, Partial Differential Equations, Difference and Functional Equations, Calculus of Variations and Optimal Control; Optimization