Convergence of a Time Discretisation for Doubly Nonlinear Evolution Equations of Second Order

The convergence of a time discretisation with variable time steps is shown for a class of doubly nonlinear evolution equations of second order. This also proves existence of a weak solution. The operator acting on the zero-order term is assumed to be the sum of a linear, bounded, symmetric, strongly positive operator and a nonlinear operator that fulfills a certain growth and a H¨older-type continuity condition. The operator acting on the first-order time derivative is a nonlinear hemicontinuous operator that fulfills a certain growth condition and is (up to some shift) monotone and coercive. Keywords Evolution equation of second order · monotone operator · weak solution · time discretisation · variable time grid · convergence Mathematics Subject Classification (2000) 65M12 · 47J35 · 34G20 · 35G25 · 35L70 · 35L90 · 47H05

• Type: Journal
• Year: 2010
• Where: FOCM
• Authors: Etienne Emmrich, Mechthild Thalhammer
• Keywords: Evolution Equation, FOCM 2010, Operator, Time Discretisation