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Regular and singular perturbations of an abstract Euler-Poisson-Darboux equation. (English. Russian original) Zbl 0968.34041
Math. Notes 66, No. 3, 292-298 (1999); translation from Mat. Zametki 66, No. 3, 364-371 (1999).
From the text: Suppose that in the Banach space $$\mathbb{E}$$ the Cauchy problem $u''(t)+ (k/t) u'(t)= \mathbb{A} u(t),\quad t>0,\tag{1}$ $u(0)= u_0,\quad u'(0)= 0,\tag{2}$ with a linear closed operator $$\mathbb{A}$$ is uniformly well-posed. The author considers cases when equation (1) is perturbed by terms whose coefficients depend on $$t$$, and he studies the behavior of the solution to problem (1), (2) as $$k\to 0$$ (regular perturbation), as well as the singular perturbation if a parameter $$\varepsilon\to 0$$ is introduced into the equation as a multiplier for $$u''(t)$$.

##### MSC:
 34G10 Linear differential equations in abstract spaces
Full Text:
##### References:
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