The Cauchy Problem
The Cauchy Problem
The contemporary state of the question for the correctness of the Cauchy problem is exposed for differential and pseudo-differential operators with non-homogeneous symbols. Ch.1,2 are devoted to constant coefficients, criteria for the correctness of the Cauchy problem in spaces of functions and distributions of power and exponential decrease and increase are presented. Ch.3 is devoted to the correctness of the Cauchy problem for differential equations with variable coefficients. Approaches based both on the method of the Levy parametrix and on energy estimates are surveyed. (37 references.)
Cauchy problem, correctness, Initial value problems for PDEs with pseudodifferential operators, energy estimates, constant coefficients, non-homogeneous symbols, General existence and uniqueness theorems (PDE), Initial value problems for linear higher-order PDEs, Initial value problems for PDEs and systems of PDEs with constant coefficients, Levy parametrix
Cauchy problem, correctness, Initial value problems for PDEs with pseudodifferential operators, energy estimates, constant coefficients, non-homogeneous symbols, General existence and uniqueness theorems (PDE), Initial value problems for linear higher-order PDEs, Initial value problems for PDEs and systems of PDEs with constant coefficients, Levy parametrix
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