High Frequency Sound According to the Boltzmann Equation
High Frequency Sound According to the Boltzmann Equation
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5. Existence in a Half Space We consider the equation Icof + ^1 H + vf = K[f] (5. 1) in the half space x > 0. To obtain existence for unlimited X we cannot afford to take absolute values and ignore the oscillations induced by 00 (in particular, there is no exis- tence theorem for steady solutions, 00 = 0, in the half space X > 0). We can use 00 effectively only by taking a Fourier or Laplace transform in x. The parameter 03 will reduce the amplitude of the transformed f in frequency space excep...t at certain resonant points. We cannot afford to use a maximum norm alone, for K has norm larger than one and cd does not reduce the amplitude uniformly. An Lp norm will be reduced by cu and, as in the previous section, can be used to reduce the maximum norm as well.
Assuming that f is bounded as x — >
What to read after High Frequency Sound According to the Boltzmann Equation?
You can find similar books in the "Read Also" column, or choose other free books by Harold Grad to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
5. Existence in a Half Space We consider the equation Icof + ^1 H + vf = K[f] (5. 1) in the half space x > 0. To obtain existence for unlimited X we cannot afford to take absolute values and ignore the oscillations induced by 00 (in particular, there is no exis- tence theorem for steady solutions, 00 = 0, in the half space X > 0). We can use 00 effectively only by taking a Fourier or Laplace transform in x. The parameter 03 will reduce the amplitude of the transformed f in frequency space excep...t at certain resonant points. We cannot afford to use a maximum norm alone, for K has norm larger than one and cd does not reduce the amplitude uniformly. An Lp norm will be reduced by cu and, as in the previous section, can be used to reduce the maximum norm as well.
Assuming that f is bounded as x — >
What to read after High Frequency Sound According to the Boltzmann Equation?
You can find similar books in the "Read Also" column, or choose other free books by Harold Grad to read onlineMoreLess
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