A note on the parabolic equation with an arbitrary parameter at the derivative

作者：Ashyralyev Allaberen; Sozen Yasar^*

来源：Mathematical and Computer Modelling, 2011, 54(11-12): 2565-2572.

DOI：10.1016/j.mcm.2011.06.028

• Abstract parabolic equation
• Coercivity inequality
• Stability inequality
• Well-posedness
• Uniform difference scheme

We consider the parabolic differential equation
epsilon u'(t) + Au(t) = f(t), -infinity < t < infinity, (0, 1)
in a Banach space E with a strongly positive operator A and with an arbitrary positive parameter epsilon. We establish the well-posedness in difference analogue of Holder space of the high order uniform difference scheme for (0.1). Moreover, in applications, the convergence estimates for the solutions of uniform difference schemes of the multidimensional parabolic differential equations with an arbitrary positive parameter epsilon are obtained.

• 出版日期2011-12