Cauchy problem

English Etymology After French mathematician Augustin Louis Cauchy. Noun en mathematics analysis For a given m-order partial differential equation, the problem of finding a solution function on that satisfies the boundary conditions that, for a smooth manifold , and , , , given specified functions defined on, and vector normal to, the manifold. en 2006 Victor Isakov Inverse Problems for Partial Differential Equations 2nd https://books.google.com.au/books?id=K_aNMWE5O38C&pg=PA41&dq=%22Cauchy+problem%22&hl=en&sa=X&ved=0ahUKEwio6ZfJi7jWAhXGgrwKHWOrBzYQ6AEIugIwMw#v=onepage&q=%22Cauchy%20problem%22&f=false 41 Springer In this chapter we formulate and in many cases prove results on uniqueness and stability of solutions of the Cauchy problem for general partial differential equations. en 2006 S. Albeverio; Ya. Belopolskaya Probabilistic Interpretation of the VV-Method for PDE Systems Olga S. Rozanova Analytical Approaches to Multidimensional Balance Laws Nova Science Publishers https://books.google.com.au/books?id=1Nl8xXe4HqYC&pg=PA2&dq=%22Cauchy+problem%22&hl=en&sa=X&ved=0ahUKEwio6ZfJi7jWAhXGgrwKHWOrBzYQ6AEIrQIwMQ#v=onepage&q=%22Cauchy%20problem%22&f=false 2 To emphasize the similarity between the characteristic method and the probabilistic approach we recall that the method of characteristics allows [one] to reduce the Cauchy problem for a first order PDE to a Cauchy problem for an ODE while the probabilistic approach allows [one] to reduce the Cauchy problem for a second order PDE to a Cauchy problem for an SDE (stochastic differential equation). en 2014 Tatsuo Nishitani Hyperbolic Systems with Analytic Coefficients: Well-posedness of the Cauchy Problem https://books.google.com.au/books?id=lOK5BQAAQBAJ&pg=PR5&dq=%22Cauchy+problem%22&hl=en&sa=X&ved=0ahUKEwio6ZfJi7jWAhXGgrwKHWOrBzYQ6AEI8AEwJw#v=onepage&q=%22Cauchy%20problem%22&f=false v Springer In this monograph we discuss the well-posedness of the Cauchy problem for hyperbolic systems. Usage notes The hypersurface S is called the en Cauchy surface. The functions fk defined on S are collectively known as the en Cauchy data of the problem. Translations class of problem involving simultaneous PDEs Bulgarian: bg задача на Коши f Italian: it problema di Cauchy m Polish: pl zagadnienie Cauchy'ego n Further reading Cauchy boundary condition Cauchy-Kowalevski theorem en Differential equations Geometry Topology en eponyms