Continuous dependence inequalities for a class of quasilinear parabolic problems

作者: L. E. Payne , G. A. Philippin , A. Safoui

DOI: 10.1007/S00033-005-0046-1

关键词: MathematicsNonlinear systemClass (set theory)Mathematical analysisValue (mathematics)

摘要: In this paper, we establish continuous dependence inequalities for the solutions u(x, t) of a class nonlinear parabolic initial-boundary value problems and their gradients when data are subject to variations.

参考文章(5)
Avner Friedman, Remarks on the maximum principle for parabolic equations and its applications. Pacific Journal of Mathematics. ,vol. 8, pp. 201- 211 ,(1958) , 10.2140/PJM.1958.8.201
Louis Nirenberg, A strong maximum principle for parabolic equations Communications on Pure and Applied Mathematics. ,vol. 6, pp. 167- 177 ,(1953) , 10.1002/CPA.3160060202
L. E. Payne, G. A. Philippin, S. Vernier Piro, Decay bounds for solutions of second order parabolic problems and their derivatives IV Applicable Analysis. ,vol. 85, pp. 293- 302 ,(2005) , 10.1080/00036810500276530
J. M. BALL, REMARKS ON BLOW-UP AND NONEXISTENCE THEOREMS FOR NONLINEAR EVOLUTION EQUATIONS Quarterly Journal of Mathematics. ,vol. 28, pp. 473- 486 ,(1977) , 10.1093/QMATH/28.4.473
L. E. Payne, G. A. Philippin, Decay bounds for solutions of second order parabolic problems and their derivatives II Mathematical Inequalities & Applications. pp. 543- 549 ,(2004) , 10.7153/MIA-07-55