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Global existence of solution of Cauchy problem for nonlinear pseudo-parabolic equation. (English) Zbl 1156.35414

Summary: We prove that the Cauchy problem for the nonlinear pseudo-parabolic equation

v t -αv xxt -βv xx +γv x +f(v) x =φ(v x ) x +g(v)-αg(v) xx

admits a unique global generalized solution in C 1 ([0,);H s ()), a unique global classical solution and asymptotic behavior of the solution. We also prove that the Cauchy problem for the equation

v t -αv xxt -βv xx =g(v)-αg(v) xx

has a unique global generalized solution in C 1 ([0,);W m,p ()L ()), a unique global classical solution and asymptotic behavior of the solution.

MSC:
35K70Ultraparabolic equations, pseudoparabolic equations, etc.
35K25Higher order parabolic equations, general
35K55Nonlinear parabolic equations
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