Formation of singularities for viscosity solutions of Hamilton-Jacobi equations in one space variable
نویسندگان
چکیده
منابع مشابه
Global Propagation of Singularities for Time Dependent Hamilton-Jacobi Equations
We investigate the properties of the set of singularities of semiconcave solutions of Hamilton-Jacobi equations of the form ut(t, x) +H(∇u(t, x)) = 0, a.e. (t, x) ∈ (0,+∞)×Ω ⊂ R n+1 . (1) It is well known that the singularities of such solutions propagate locally along generalized characteristics. Special generalized characteristics, satisfying an energy condition, can be constructed, under som...
متن کاملGeometrical Solutions of Hamilton-jacobi Equations
The concept of the geometrical solution of Hamilton-Jacobi equations in arbitrary space dimension is introduced. The characterization of such solution is based on the intersection of several invariant hyper-surfaces in the space of 1-jets. This solution notion allows not only for the smooth evolution beyond the usual singularity formation but also for superposition of underlying geometrical sol...
متن کاملA Level Set Method for the Computation of Multivalued Solutions to Quasi-linear Hyperbolic Pdes and Hamilton-jacobi Equations
We develop a level set method for the computation of multivalued solutions to quasi-linear hyperbolic partial differential equations and Hamilton-Jacobi equations in any number of space dimensions. We use the classic idea of Courant and Hilbert to define the solution of the quasi-linear hyperbolic PDEs or the gradient of the solution to the Hamilton-Jacobi equations as zero level sets of level ...
متن کاملFormation of singularities for viscosity solutions of Hamilton-Jacobi equations in higher dimensions
In this work we study the generation of singularities (shock waves) of the solution of the Cauchy problem for HamiltonJacobi equations in several space variables, under no assumption on convexity or concavity of the hamiltonian. We study the problem in the class of viscosity solutions, which are the correct class of weak solutions. We first examine the way the characteristics cross by identifyi...
متن کاملHamilton-jacobi Equations in the Wasserstein Space
Abstract. We introduce a concept of viscosity solutions for Hamilton-Jacobi equations (HJE) in the Wasserstein space. We prove existence of solutions for the Cauchy problem for certain Hamiltonians defined on the Wasserstein space over the real line. In order to illustrate the link between HJE in the Wasserstein space and Fluid Mechanics, in the last part of the paper we focus on a special Hami...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015