J. Aust. Math. Soc.
74 (2003), 69-86
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Generalized quasilinear hyperbolic equations and Yosida approximations
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Jong Yeoul Park
Department of Mathematics
Pusan National University
Pusan 609-735
Korea
jyepark@pusan.ac.kr
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Il Hyo Jung
Department of Mathematics
Pusan National University
Pusan 609-735
Korea
ilhjung@pusan.ac.kr
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Yong Han Kang
Department of Mathematics
Pusan National University
Pusan 609-735
Korea
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Abstract
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We will show the existence, uniqueness and
regularity of global solutions for the Cauchy
problem for nonlinear evolution equations with
the damping term
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![\[u''(t) + M(|A^{1/2} u(t)|^2)Au(t)
+ \delta u'(t) = f(t) \quad (\delta > 0).\]](img_files_abstracts/j42-img0.png)
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As an application of our results, we give the
global solvability and regularity of the mixed
problem with Dirichlet boundary conditions:
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![\[ u''(x,t) +(-1)^k M\left(
\int_{\Omega} |\nabla^k u(x,t)|^2\,dx\right) \Delta^k u(x,t)
+ \delta u'(x,t) =f(x,t).\]](img_files_abstracts/j42-img1.png)
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