Evolution governed by “generalized“ dissipative operators

Evolution Equations Governed by Elliptic Operators

Fractional Evolution Equations Governed by Coercive Differential Operators

and Applied Analysis 3 2. α-Times Regularized Resolvent Family Throughout this paper, X is a complex Banach space, and we denote by B X the algebra of all bounded linear operators on X. Let A be a closed densely defined operator on X, let D A and R A be its domain and range, respectively, and let α ∈ 0, 2 , C ∈ B X be injective. Define ρC A : {λ ∈ C : λ − A is injective and R C ⊂ R λ − A }. Let...

On the evolution of localized wave packets governed by a dissipative wave equation

The present paper deals with the effect of dissipation on the propagation of wave packets governed by a wave equation of Jeffrey type. We show that all packets undergo a shift of the central frequency (the mode with maximal amplitude) towards the lower frequencies (‘‘redshift’’ in theory of light or ‘‘baseshift’’ in acoustics). Packets with Gaussian apodization function do not change their shap...

Nonlinear Evolution Governed by Accretive Operators in Banach Spaces: Error Control and Applications

Nonlinear evolution equations governed by m-accretive operators in Banach spaces are discretized via the backward or forward Euler methods with variable stepsize. Computable a posteriori error estimates are derived in terms of the discrete solution and data, and shown to converge with optimal order O( √ τ). Applications to scalar conservation laws and degenerate parabolic equations (with or wit...

Editorial: Could Speciation Across Evolution be Governed by Genetic Switch Codes at Short Tandem Repeats?