Critical exponent for the Cauchy problem to the weakly coupled damped wave system
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Publication:2509657
DOI10.1016/j.na.2014.06.001zbMath1297.35133OpenAlexW2078581129MaRDI QIDQ2509657
Kenji Nishihara, Yuta Wakasugi
Publication date: 29 July 2014
Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.na.2014.06.001
Critical exponents in context of PDEs (35B33) Second-order semilinear hyperbolic equations (35L71) Initial value problems for second-order hyperbolic systems (35L52)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Asymptotic behavior of solutions for a system of semilinear heat equations and the corresponding damped wave system
- Global existence of solutions for a system of nonlinear damped wave equations.
- Large time behavior of solutions for a system of nonlinear damped wave equations
- Damped wave equation with super critical nonlinearities.
- Existence and nonexistence of global solutions for a nonlinear hyperbolic system with damping
- Global existence and nonexistence of solutions for a system of nonlinear damped wave equations
- Boundedness and blow up for a semilinear reaction-diffusion system
- On the asymptotic behavior of solutions of semi-linear wave equations
- Breakdown of solutions to \(\square u+u_ t=| u| ^{1+\alpha}\)
- The \(L^{p}\)--\(L^{q}\) estimates of solutions to one-dimensional damped wave equations and their application to the compressible flow through porous media
- \(L^p\)-\(L^q\) estimates of solutions to the damped wave equation in 3-dimensional space and their application
- Global existence of solutions for semilinear damped wave equations in \(\mathbb R^N\) with noncompactly supported initial data
- Existence and nonexistence of global solutions of higher-order parabolic problems with slow decay initial data
- Large time behavior and \(L^{p}\)-\(L^{q}\) estimate of solutions of 2-dimensional nonlinear damped wave equations
- \(L^p\)-\(L^q\) estimates for damped wave equations and their applications to semi-linear problem
- Global solutions to the Cauchy problem for the weakly coupled system of damped wave equations
- Lifespan estimates for solutions of some evolution inequalities
- A blow-up result for a nonlinear wave equation with damping: The critical case
- Selfsimilar profiles in large time asymptotics of solutions to damped wave equations
- On nonexistence of global solutions of some semilinear parabolic differential equations
- A note on the lifespan of solutions to the semilinear damped wave equation
- On the diffusion phenomenon of quasilinear hyperbolic waves
- Critical exponent for a nonlinear wave equation with damping
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