Integral Geometry and Inverse Problems for Hyperbolic Equations
V. G. Romanov
Apr 2013 · Springer Tracts in Natural Philosophy Book 26 · Springer Science & Business Media
Ebook
154
Pages
reportRatings and reviews aren’t verified Learn More
About this ebook
There are currently many practical situations in which one wishes to determine the coefficients in an ordinary or partial differential equation from known functionals of its solution. These are often called "inverse problems of mathematical physics" and may be contrasted with problems in which an equation is given and one looks for its solution under initial and boundary conditions. Although inverse problems are often ill-posed in the classical sense, their practical importance is such that they may be considered among the pressing problems of current mathematical re search. A. N. Tihonov showed [82], [83] that there is a broad class of inverse problems for which a particular non-classical definition of well-posed ness is appropriate. This new definition requires that a solution be unique in a class of solutions belonging to a given subset M of a function space. The existence of a solution in this set is assumed a priori for some set of data. The classical requirement of continuous dependence of the solution on the data is retained but it is interpreted differently. It is required that solutions depend continuously only on that data which does not take the solutions out of M.
Rate this ebook
Tell us what you think.
Reading information
Smartphones and tablets
Install the Google Play Books app for Android and iPad/iPhone. It syncs automatically with your account and allows you to read online or offline wherever you are.
Laptops and computers
You can listen to audiobooks purchased on Google Play using your computer's web browser.
eReaders and other devices
To read on e-ink devices like Kobo eReaders, you'll need to download a file and transfer it to your device. Follow the detailed Help Center instructions to transfer the files to supported eReaders.
