Double-Scale Gevrey Asymptotics for Logarithmic Type Solutions to Singularly Perturbed Linear Initial Value Problems
Keyword(s):
We examine a family of linear partial differential equations both singularly perturbed in a complex parameter and singular in complex time at the origin. These equations entail forcing terms which combine polynomial and logarithmic type functions in time and that are bounded holomorphic on horizontal strips in one complex space variable. A set of sectorial holomorphic solutions are built up by means of complete and truncated Laplace transforms w.r.t time and parameter and Fourier inverse integral in space. Asymptotic expansions of these solutions relatively to time and parameter are investigated and two distinguished Gevrey type expansions in monomial and logarithmic scales are exhibited.
2010 ◽
Vol 234
(12)
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pp. 3445-3457
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2016 ◽
Vol 284
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pp. 169-174
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1989 ◽
Vol 49
(1)
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pp. 1-25
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1971 ◽
pp. 111-152
Numerical investigation for solutions and derivatives of singularly perturbed initial value problems
2021 ◽
Vol 11
(2)
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pp. 123
Keyword(s):
1957 ◽
Vol 33
(1)
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pp. 31-36
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