Displaying similar documents to “Nonlocal problems for first order functional partial differential equations”

Decay rates of Volterra equations on ℝN

Monica Conti, Stefania Gatti, Vittorino Pata (2007)

Open Mathematics

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This note is concerned with the linear Volterra equation of hyperbolic type ∂ t t u ( t ) - α Δ u ( t ) + ∫ 0 t μ ( s ) Δ u ( t - s ) d s = 0 on the whole space ℝN. New results concerning the decay of the associated energy as time goes to infinity were established.

Semilinear evolution equations of the parabolic type

Jan Bochenek (1999)

Annales Polonici Mathematici

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This paper is devoted to the investigation of the abstract semilinear initial value problem du/dt + A(t)u = f(t,u), u(0) = u₀, in the "parabolic" case.

On the Cauchy problem for linear hyperbolic functional-differential equations

Alexander Lomtatidze, Jiří Šremr (2012)

Czechoslovak Mathematical Journal

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We study the question of the existence, uniqueness, and continuous dependence on parameters of the Carathéodory solutions to the Cauchy problem for linear partial functional-differential equations of hyperbolic type. A theorem on the Fredholm alternative is also proved. The results obtained are new even in the case of equations without argument deviations, because we do not suppose absolute continuity of the function the Cauchy problem is prescribed on, which is rather usual assumption...