This monograph deals with the inverse problems of determining a variable coefficient and right side for hyperbolic and parabolic equations on the basis of known solutions at fixed points of space for all times. The problems are one-dimensional in nature since the desired coefficient of the equation is a function of only one coordinate, while the desired right side is a function only of time. The authors use methods based on the spectral theory of ordinary differential operators of second order and also methods which make it possible to reduce the investigation of the inverse problems to the investigation of nonlinear operator equations.The problems studied have applied importance, since they are models for interpreting data of geophysical prospecting by seismic and electric means. In the first chapter, the authors prove the one-to-one correspondence between solutions of direct Cauchy problems for equations of different types, and they present the solution of an inverse problem of heat conduction. In the second chapter they consider a second-order hyperbolic equation describing a wave process in three-dimensional half-space. The third chapter investigates formulations of one-dimensional inverse problems for the wave equation in multidimensional space.
Publisher: American Mathematical Society
Number of pages: 70
You may also be interested in...
£19.25Mixed media product
Please sign in to write a review
Simply reserve online and pay at the counter when you collect. Available in shop from just two hours, subject to availability.
Thank you for your reservation
Your order is now being processed and we have sent a confirmation email to you at
When will my order be ready to collect?
Following the initial email, you will be contacted by the shop to confirm that your item is available for collection.
Call us on or send us an email at
Unfortunately there has been a problem with your order
Please try again or alternatively you can contact your chosen shop on or send us an email at