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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Asymptotic Methods for Investigating Quasiwave Equations of Hyperbolic Type (Hardcover, 1997 ed.)
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Asymptotic Methods for Investigating Quasiwave Equations of Hyperbolic Type (Hardcover, 1997 ed.)
Series: Mathematics and Its Applications, 402
Expected to ship within 10 - 15 working days
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The theory of partial differential equations is a wide and rapidly
developing branch of contemporary mathematics. Problems related to
partial differential equations of order higher than one are so
diverse that a general theory can hardly be built up. There are
several essentially different kinds of differential equations
called elliptic, hyperbolic, and parabolic. Regarding the
construction of solutions of Cauchy, mixed and boundary value
problems, each kind of equation exhibits entirely different
properties. Cauchy problems for hyperbolic equations and systems
with variable coefficients have been studied in classical works of
Petrovskii, Leret, Courant, Gording. Mixed problems for hyperbolic
equations were considered by Vishik, Ladyzhenskaya, and that for
general two dimensional equations were investigated by Bitsadze,
Vishik, Gol'dberg, Ladyzhenskaya, Myshkis, and others. In last
decade the theory of solvability on the whole of boundary value
problems for nonlinear differential equations has received
intensive development. Significant results for nonlinear elliptic
and parabolic equations of second order were obtained in works of
Gvazava, Ladyzhenskaya, Nakhushev, Oleinik, Skripnik, and others.
Concerning the solvability in general of nonlinear hyperbolic
equations, which are connected to the theory of local and nonlocal
boundary value problems for hyperbolic equations, there are only
partial results obtained by Bronshtein, Pokhozhev, Nakhushev."
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