Global well-posedness and stability of a partial integro-differential equation with applications to viscoelasticity

S.-O. Londen, H. Petzeltová and J. Prüss
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S.-O. Londen: Helsinki University of Technology, Institute of Mathematics
H. Petzeltová: Czech Academy of Sciences Žitná 25, Institute of Mathematics
J. Prüss: Martin-Luther-Universität Halle-Wittenberg, FB Mathematik und Informatik

A chapter in Nonlinear Evolution Equations and Related Topics, 2003, pp 169-201 from Springer

Abstract: Abstract In this paper we consider the equation (1.1) $$ {u_{{tt}}}(t,x) = \int_{0}^{t} {a(t - s){u_{{txx}}}(s.x)ds + \frac{d}{{dt}}\int_{0}^{t} {b(t - s)(g{{({u_{x}}(s,x))}_{x}}ds + f(t,x),} } $$ t > 0, x ∈ (0, 1), with boundary conditions (1.2) $$ u(t,0) = u(t,1) = 0,t > 0, $$ and initial values (1.3) $$ u(0,x) = {u^{0}}(x),{u_{t}}(0,x) = {u^{1}}(x). $$

Keywords: Global Existence; Global Asymptotic Stability; Energy Inequality; Unique Weak Solution; Global Classical Solution (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-7924-8_9

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DOI: 10.1007/978-3-0348-7924-8_9

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