In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function.
In mathematics, a hyperbolic partial differential equation of order is a partial differential equation (PDE) that, roughly speaking, has a well-posed initial value problem for the first derivatives. More precisely, the Cauchy problem can be locally solved for arbitrary initial data along any non-characteristic hypersurface. Many of the equations of mechanics are hyperbolic, and so the study of hyperbolic equations is of substantial contemporary interest. The model hyperbolic equation is the wave equation. In one spatial dimension, this is
Numerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs).
Jürgen Kurt Moser was a German-American mathematician, honored for work spanning over four decades, including Hamiltonian dynamical systems and partial differential equations.
Louis Nirenberg was a Canadian-American mathematician, considered one of the most outstanding mathematicians of the 20th century.
Luis Ángel Caffarelli is an Argentine-American mathematician. He studies partial differential equations and their applications.
In mathematics, the viscosity solution concept was introduced in the early 1980s by Pierre-Louis Lions and Michael G. Crandall as a generalization of the classical concept of what is meant by a 'solution' to a partial differential equation (PDE). It has been found that the viscosity solution is the natural solution concept to use in many applications of PDE's, including for example first order equations arising in dynamic programming, differential games or front evolution problems, as well as second-order equations such as the ones arising in stochastic optimal control or stochastic differential games.
In mathematics, a (real) Monge–Ampère equation is a nonlinear second-order partial differential equation of special kind. A second-order equation for the unknown function u of two variables x,y is of Monge–Ampère type if it is linear in the determinant of the Hessian matrix of u and in the second-order partial derivatives of u. The independent variables (x,y) vary over a given domain D of R2. The term also applies to analogous equations with n independent variables. The most complete results so far have been obtained when the equation is elliptic.
Vladimir Gilelevich Maz'ya is a Russian-born Swedish mathematician, hailed as "one of the most distinguished analysts of our time" and as "an outstanding mathematician of worldwide reputation", who strongly influenced the development of mathematical analysis and the theory of partial differential equations.
Avner Friedman is Distinguished Professor of Mathematics and Physical Sciences at Ohio State University. His primary field of research is partial differential equations, with interests in stochastic processes, mathematical modeling, free boundary problems, and control theory.
Xu-Jia Wang is a Chinese-Australian mathematician. He is a professor of mathematics at the Australian National University and a fellow of the Australian Academy of Science.
James Burton Serrin was an American mathematician, and a professor at University of Minnesota.
Willi Jäger is a German mathematician.
In mathematics, k-Hessian equations are partial differential equations (PDEs) based on the Hessian matrix. More specifically, a Hessian equation is the k-trace, or the kth elementary symmetric polynomial of eigenvalues of the Hessian matrix. When k ≥ 2, the k-Hessian equation is a fully nonlinear partial differential equation. It can be written as , where , , and , are the eigenvalues of the Hessian matrix and , is a th elementary symmetric polynomial.
Gregory Eskin is a Russian-Israeli-American mathematician, specializing in partial differential equations.
Héctor Chang Lara is a Venezuelan mathematician working at CIMAT, Guanajuato unit, in Mexico. Chang received his BA in Mathematics from Simon Bolivar University in Venezuela, his MS from the University of New Mexico and his PhD in mathematics from the University of Texas at Austin, advised by Luis Caffarelli. Chang works in partial differential equations, specializing in elliptic and parabolic differential equations as well as integro-differential equations and free boundary problems.
Robert Ronald Jensen is an American mathematician, specializing in nonlinear partial differential equations with applications to physics, engineering, game theory, and finance.
Christoph Schwab is a German applied mathematician, specializing in numerical analysis of partial differential equations and boundary integral equations.
Xavier Ros Oton is a Spanish mathematician who works on partial differential equations (PDEs). He is an ICREA Research Professor and a Full Professor at the University of Barcelona.
Joel Spruck is a mathematician, J. J. Sylvester Professor of Mathematics at Johns Hopkins University, whose research concerns geometric analysis and elliptic partial differential equations. He obtained his PhD from Stanford University with the supervision of Robert S. Finn in 1971.
