期刊论文详细信息
Proceedings Mathematical Sciences | |
Formula for a Solution of ð‘¢ð‘¡ + ð»(ð‘¢, Dð‘¢) = ð‘” | |
G D Veerappa Gowda1  Adimurthi2  | |
[1] $$;TIFR Centre, P.B. , Indian Institute of Science Campus, Bangalore 0 0, India$$ | |
关键词: Hamilton-Jacobi equation; dynamic programming principle; viscosity sub and super solutions.; | |
DOI : | |
学科分类:数学(综合) | |
来源: Indian Academy of Sciences | |
【 摘 要 】
We study the continuous as well as the discontinuous solutions of Hamilton–Jacobi equation ð‘¢ð‘¡ + ð»(ð‘¢, Dð‘¢) = ð‘” in $mathbb{R}^n × mathbb{R}_+$ with ð‘¢(ð‘¥, 0)=ð‘¢0(ð‘¥). The Hamiltonian ð»(ð‘ , ð‘) is assumed to be convex and positively homogeneous of degree one in ð‘ for each ð‘ in $mathbb{R}$. If ð» is non increasing in ð‘ , in general, this problem need not admit a continuous viscosity solution. Even in this case we obtain a formula for discontinuous viscosity solutions.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO201912040506506ZK.pdf | 162KB | download |