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On a hyperbolic quenching problem in several dimensions. (English) Zbl 0687.35056
The author is concerned with the Cauchy problem for the hyperbolic equation $(E)\quad u_{tt}=\Delta_ nu+\epsilon f(u)\quad in\quad D\times (0,T),\quad D\subset {\mathbb{R}}^ n,\quad n=1,2,3.$ By a standard device, (E) is written as an equivalent system in the Hilbert space $$H^ 1_ 0(D)\times L_ 2(D)$$, associated with one-parameter groups generators.
Reviewer: N.Pavel

MSC:
 35L70 Second-order nonlinear hyperbolic equations 35L15 Initial value problems for second-order hyperbolic equations 47F05 General theory of partial differential operators 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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