Geodesic
Blow-up of weak solutions for the semilinear wave equations with nonlinear boundary and interior sources and damping
Lorena Bociu1 ; Irena Lasiecka2
1 243 Avery Hall University of Nebraska-Lincoln Lincoln, NE 68588, U.S.A.
2 Department of Mathematics University of Virginia Charlottesville, VA 22904, U.S.A.
Applicationes Mathematicae, Tome 35 (2008) no. 3, pp. 281-304 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We focus on the blow-up in finite time of weak solutions to the wave equation with interior and boundary nonlinear sources and dissipations. Our central interest is the relationship of the sources and damping terms to the behavior of solutions. We prove that under specific conditions relating the sources and the dissipations (namely $p > m$ and $k > m$), weak solutions blow up in finite time.
DOI : 10.4064/am35-3-3
Keywords: focus blow up finite time weak solutions wave equation interior boundary nonlinear sources dissipations central interest relationship sources damping terms behavior solutions prove under specific conditions relating sources dissipations namely weak solutions blow finite time

Lorena Bociu 1 ; Irena Lasiecka 2

1 243 Avery Hall University of Nebraska-Lincoln Lincoln, NE 68588, U.S.A.
2 Department of Mathematics University of Virginia Charlottesville, VA 22904, U.S.A. 
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     title = {Blow-up of weak solutions for the semilinear
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     journal = {Applicationes Mathematicae},
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 interior sources and damping
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 interior sources and damping
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Lorena Bociu; Irena Lasiecka. Blow-up of weak solutions for the semilinear
 wave equations with nonlinear boundary and
 interior sources and damping. Applicationes Mathematicae, Tome 35 (2008) no. 3, pp. 281-304. doi: 10.4064/am35-3-3

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