Results 301 to 310 of about 5,378,040 (354)
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1986
In this chapter we introduce the wave equation, formulate initial-boundary value problems, and prove uniqueness and existence via the spectral theorem. To get more information about the behaviour of the solutions, we have to study the spectrum of the underlying operators more carefully, which will be done in Chapter 4.
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In this chapter we introduce the wave equation, formulate initial-boundary value problems, and prove uniqueness and existence via the spectral theorem. To get more information about the behaviour of the solutions, we have to study the spectrum of the underlying operators more carefully, which will be done in Chapter 4.
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2019
In the previous chapter, the concept of sound was introduced and a simple example of a physical system that can produce sound was given. More specifically, we saw how a metal bar struck by a hammer exhibits a displacement over time that is sinusoidal in nature.
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In the previous chapter, the concept of sound was introduced and a simple example of a physical system that can produce sound was given. More specifically, we saw how a metal bar struck by a hammer exhibits a displacement over time that is sinusoidal in nature.
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2020
In Chaps. 29 and 30, you have seen how Fourier and Laplace transforms help us solve Poisson’s equation and the diffusion equation. We turn our attention now to another very important equation of mathematical physics, the wave equation. As you might expect, this is a well-studied topic with a vast literature.
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In Chaps. 29 and 30, you have seen how Fourier and Laplace transforms help us solve Poisson’s equation and the diffusion equation. We turn our attention now to another very important equation of mathematical physics, the wave equation. As you might expect, this is a well-studied topic with a vast literature.
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1964
According to (1.24), the wave equation in R 1 is of the form $$ {u_{xx}} - \frac{1} {{{\gamma |2}}}{u_{tt}} = 0,\quad where\quad \gamma = const > 0 $$ (2.1) The symbol x denotes a real variable here. Introduction of a new time scale t = γt shows that we may restrict ourselves to the case γ = 1.
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According to (1.24), the wave equation in R 1 is of the form $$ {u_{xx}} - \frac{1} {{{\gamma |2}}}{u_{tt}} = 0,\quad where\quad \gamma = const > 0 $$ (2.1) The symbol x denotes a real variable here. Introduction of a new time scale t = γt shows that we may restrict ourselves to the case γ = 1.
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1998
This chapter treats the equation $$\frac{{{\partial ^2}u}}{{\partial {t^2}}}\left( {x,t} \right) - {\omega ^2}\Delta u\left( {x,t} \right) = f\left( {x,t} \right),x \in \Omega ,t \in \left( {0,T} \right)$$ (1) which is called the wave equation and plays an important role in mathematical physics.
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This chapter treats the equation $$\frac{{{\partial ^2}u}}{{\partial {t^2}}}\left( {x,t} \right) - {\omega ^2}\Delta u\left( {x,t} \right) = f\left( {x,t} \right),x \in \Omega ,t \in \left( {0,T} \right)$$ (1) which is called the wave equation and plays an important role in mathematical physics.
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Boundary Stabilization of Wave Equation With Velocity Recirculation
IEEE Transactions on Automatic Control, 2017Lingling Su +3 more
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2000
The term ‘wave’ is used to signify an effect which propagates in a medium. The medium can be an object such as a string, cable, beam, plate, shell or a physical space consisting of fluids, solids, etc. The most common observation of a wave is that of the motion of the surface of still water when a pebble is thrown in it. The ‘snap’ at the end of a whip
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The term ‘wave’ is used to signify an effect which propagates in a medium. The medium can be an object such as a string, cable, beam, plate, shell or a physical space consisting of fluids, solids, etc. The most common observation of a wave is that of the motion of the surface of still water when a pebble is thrown in it. The ‘snap’ at the end of a whip
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1974
Many of the earlier sections of this book may be summarised by saying that they dealt with superposition properties of waves of various kinds. As we saw in section 1.2, if it is assumed that the equation of motion of the wave is linear, the amplitude of different waves may be added.
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Many of the earlier sections of this book may be summarised by saying that they dealt with superposition properties of waves of various kinds. As we saw in section 1.2, if it is assumed that the equation of motion of the wave is linear, the amplitude of different waves may be added.
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