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Local and global nonexistence of solutions to nonlinear hyperbolic inequalities

โœ Scribed by M. Guedda

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
358 KB
Volume
16
Category
Article
ISSN
0893-9659

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โœฆ Synopsis

where t, ls a homogeneous linear partial differential operator of order m and p > 1. For example, we prove that for any T > 0 the problem, with ut(x,O) = ~1, cp(r) = lrlQ-%, 0 < q 5 1 and h(x) = 1x17, 7 > 0, has no solution if liml,+m ,,(x)lxl7q/(p-q) = 00.

๐Ÿ“œ SIMILAR VOLUMES

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We give an example of the influence of the dependence of the coefficient of equation on time variable, and in particular oscillations in time, on a global existence of the solution to the nonlinear hyperbolic equation. Namely for arbitrary small initial data we construct a blowing up solution.

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The results of this paper are contained in a doctoral thesis submitted to the Graduate School of Arts and Sciences of New York University. Reproduction in whole or in part is permitted for any purpose of the United States Government.