The Cauchy Problem for Hyperbolic Operators

The Cauchy Problem for Hyperbolic Operators

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The goal of this book is a construction of the fundamental solution to the Cauchy problem for hyperbolic operators with multiple characteristics. Well-posedness of the problem in various functional spaces as well as a propagation of singularities of the solutions are investigated, too. Levy conditions described in the book allow to construct fundamental solutions. The approach represented in the book is essentially based on the zeros of the complete symbol of the operator. For operators with variable coefficients hyperbolicity conditions are formulated by means of these zeros similarly to Hadamard's conditions for operators with constant coefficient. This approach needs Fourier integral operators with inhomogeneous phase functions. Necessary knowledge on these ones is given, too.JV). Further, we calculate the symbol of the operator B(1) - (Dt-V + B)(I + Af{l))-(I + Af{1))(Dt-V + fM), = Bx + Bt- [V, MW] - ^(0) - ^^fl1) + BMW - M^^ . According to the main properties of the symbol class SPis{mi, m2, Tu^m.n and to our choice of M^\ anbsp;...

Title:The Cauchy Problem for Hyperbolic Operators
Author: Karen Yagdjian
Publisher:John Wiley & Sons Incorporated - 1997

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