The Cauchy problem for the Hamilton-Jacobi equation, which appears in molecular biology for the Crow-Kimura model of molecular evolution, is considered. The state characteristics of the equation that start in a given initial manifold bounded in the state space stay in a strip bounded in the state variable and fill a part of this strip. The values attained by the impulse characteristics on a finite time interval are arbitrarily large in magnitude. We propose a construction of a smooth extension for a continuous minimax/viscosity solution of the problem to the part of the strip that is not covered by the characteristics starting in the initial manifold.
|投稿的翻译标题||Construction of a continuous minimax/viscosity solution of the Hamilton-Jacobi-Bellman equation with nonextendable characteristics|
|期刊||Труды института математики и механики УрО РАН|
|州||Published - 2014|
- 27.00.00 MATHEMATICS
Level of Research Output
- VAK List