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- W3103179436 abstract "The aim of this paper is to study the problem $$left{begin{array}{ll} u_{tt}-Delta u+P(x,u_t)=f(x,u) quad & {rm in} , (0,infty)timesOmega, u=0 & {rm on} , (0,infty)times Gamma_0, u_{tt}+partial_nu u-Delta_Gamma u+Q(x,u_t)=g(x,u)quad & {rm on} , (0,infty)times Gamma_1, u(0,x)=u_0(x),quad u_t(0,x)=u_1(x) & {rm in} , overline Omega, end{array}right.$$ where $${Omega}$$ is a open bounded subset of $${{mathbb R}^N}$$ with C 1 boundary ( $${N ge 2}$$ ), $${Gamma = partialOmega}$$ , $${(Gamma_{0},Gamma_{1})}$$ is a measurable partition of $${Gamma}$$ , $${Delta_{Gamma}}$$ denotes the Laplace–Beltrami operator on $${Gamma}$$ , $${nu}$$ is the outward normal to $${Omega}$$ , and the terms P and Q represent nonlinear damping terms, while f and g are nonlinear subcritical perturbations. In the paper a local Hadamard well-posedness result for initial data in the natural energy space associated to the problem is given. Moreover, when $${Omega}$$ is C 2 and $${overline{Gamma_{0}} cap overline{Gamma_{1}} = emptyset}$$ , the regularity of solutions is studied. Next a blow-up theorem is given when P and Q are linear and f and g are superlinear sources. Finally a dynamical system is generated when the source parts of f and g are at most linear at infinity, or they are dominated by the damping terms." @default.
- W3103179436 created "2020-11-23" @default.
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- W3103179436 date "2016-11-02" @default.
- W3103179436 modified "2023-10-16" @default.
- W3103179436 title "On the Wave Equation with Hyperbolic Dynamical Boundary Conditions, Interior and Boundary Damping and Source" @default.
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- W3103179436 doi "https://doi.org/10.1007/s00205-016-1055-2" @default.
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