|
|
- 2018
带有梯度超线性项抛物方程黏性解的比较原理
|
Abstract:
摘要： 研究梯度具有超线性增长的完全非线性抛物方程问题,证明了具有超线性增长的半连续黏性上下解的比较原理的存在,并且把此结果延伸到单调抛物系统中。
Abstract: A problem of fully nonlinear degenerate parabolic partial differential equations with a superlinear gradient nonlinearity is studied. A comparison result is proved between semicontinuous viscosity subsolutions and supersolutions having superlinear growth. We extend our result to monotone systems of parabolic equations
| [1] | CRANDALL M G, ISHII H, LIONS P-L. Users guide to viscosity solutions of second order partial differential equations[J]. Bulletin of the American Mathematical Society, 1992, 27(1):1-67. |
| [2] | ALVAREZ O. Bounded-from-below viscosity solutions of Hamilton-Jacobi equations[J]. Differential Integral Equations, 1997,10(3):419-436. |
| [3] | ISHII H. Comparison results for Hamilton-Jacobi equations without growth condition on solutions from above[J]. Applicable Analysis, 1997, 67(3-4):357-372. |
| [4] | ISHII K, TOMITA Y. Unbounded viscosity solutions of nonlinear second order PDEs[J]. Advances in Mathematical Sciences and Applications, 2000, 10(2):689-710. |
| [5] | KOIKE S, LEY O. Comparison principle for unbounded viscosity solutions of degenerate elliptic PDEs with gradient superlinear term[J]. Journal of Mathematical Analysis and Applications, 2001, 381(1):110-120. |
| [6] | DA-LIO F, LEY O. Uniqueness results for second-order Bellman-Isaacs equations under quadratic growth assumptions and applications[J]. SIAM Journal on Control and Optimization, 2006, 45(1):74-106. |
| [7] | ISHII H. Uniqueness of unbounded viscosity solution of Hamilton-Jacobi equations[J]. Indiana University Mathematics Journal, 1984, 33(5):721-748. |
| [8] | AIZAWA S, TOMITA Y. Unbounded viscosity solutions of fully nonlinear elliptic equations in <i>R<sup>n</sup></i>[J]. Advances in Mathematical Sciences and Applications, 1993,2(2):297-316. |
| [9] | DA-LIO F, LEY O. Convex Hamilton-Jacobi equations under superlinear growth conditions on data[J]. Applied Mathematics and Optimization, 2001, 63(3):309-339. |
| [10] | CRANDALL M G, ISHII H, LIONS P-L. Viscosity solutions of Hamilton-Jacobi equations[J]. Transactions of the American Mathematical Society, 1983, 277(1):1-42. |
| [11] | ISHII H, KOIKE S. Viscosity solutions for monotone systems of second-order elliptic PDEs[J]. Communications in Partial Differential Equations, 1991, 16(6):1095-1128. |
| [12] | BARLES G. Uniqueness and regularity results for first-order Hamilton-Jacobi equations[J]. Indiana University Mathematics Journal, 1990, 39(2):443-466. |
