Inverse problems in differential equations constitute a pivotal area in applied mathematics and engineering, where the aim is to deduce unknown parameters or inputs within a differential equation from ...

In the context of inverse problems, a mathematical model of the measurements is called the direct problem. To understand this term, let us consider a model for obstetric sonography. An ultrasonic ...

We examine a heat problem in 1D. Assume that a rod with given temperature distribution u_0(x) is cooled to temperature 0 on the exteriors at 0 and pi. Assume that u(x,t) for the Temperature at point x ...

Check back in Fall 2025. Abstract: Constitutive or material models provide a mathematical description of how solids respond to mechanical stimuli. For example, an isotropic linear elastic constitutive ...

University of California, Santa Cruz professor of mathematics François Monard has received the prestigious Calderón Prize for his work in the field of inverse problems. Broadly defined, researchers ...

Inverse problems research lies at the intersection of pure and applied mathematics. The forward problem corresponding to an inverse problem is usually a well defined problem in physics, engineering or ...