Synopsis
Foundations for solving Cauchy’s problem in linear partial differential equations .
This classic text presents Hadamard’s detailed approach to hyperbolic equations, their behavior, and the conditions needed to determine a unique solution from given data.
This volume surveys the theory behind Cauchy problems for hyperbolic PDEs, introducing fundamental theorems, characteristics, and the construction of elementary solutions. It blends rigorous analysis with practical methods, aiming to clarify when solutions exist and how they depend on initial data and boundary conditions. The work tracks developments from foundational ideas to methods that extend to more complex cases, including even and odd numbers of independent variables and the descent technique.- Learn how Cauchy data and boundary geometry influence the interior solution.
- Explore the role of characteristics and conoids in shaping the problem.
- See the progression from fundamental theorems to concrete formulas and constructions.
- Understand the treatment of singularities, improper integrals, and the adjoint equation in solution building.
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