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The Initial Value Problem for Hyperbolic Homogeneous Equations with Constant Coefficients

In: Plane Waves and Spherical Means

Author

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  • Fritz John

    (New York University, Courant Institute of Mathematical Sciences)

Abstract

The differential equations considered in this chapter shall be of the form (2.1) L [ u ] = Q − ( ∂ ∂ x 1 , ... , ∂ ∂ x n , ∂ ∂ t ) u = 0 $$L\,[u]\, = \,Q\left( {\frac{\partial }{{\partial {x_1}}},...,\frac{\partial }{{\partial {x_n}}},\frac{\partial }{{\partial t}}} \right)u = 0$$ where Q(η 1, ...., η n, λ) is a form of degree m in its arguments with constant real coefficients. The Cauchy problem to be solved here consists in finding a solution u of (2.1) satisfying the initial conditions for t = 0.

Suggested Citation

  • Fritz John, 1981. "The Initial Value Problem for Hyperbolic Homogeneous Equations with Constant Coefficients," Springer Books, in: Plane Waves and Spherical Means, chapter 0, pages 15-41, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-9453-2_3
    DOI: 10.1007/978-1-4613-9453-2_3
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