Sentence examples for abstract evolution from inspiring English sources

An abstract evolution equation in Hilbert spaces is considered.

For the abstract evolution equation (3), we obtain the following results.

Thus, the problem (2) is rewritten into the form of abstract evolution equation (3).

Indeed, the nonlocal Cauchy problem for abstract evolution differential equations was studied by Byszewski [17, 18] initially.

Graphical abstract Evolution of pH, Zn II) and ligand concentration during a workday in an industrial wastewater.

In particular, several authors have considered a nonlocal Cauchy problem for abstract evolution differential equations having fractional order.

Then, problem (3.65) takes the abstract neutral evolution form (3.34).

Many authors have considered abstract linear evolution equations in Banach spaces (see [19 23] and references therein).

Graphical abstract Temporal evolution of the maximum vertical displacement and average yearly rate of height change.

Wang and Wang [23] investigated monotone iterative techniques for abstract semilinear evolution equations.

Moreover, Diagana studied the existence of pseudo-almost periodic solutions to the abstract semilinear evolution equation.