Global existence and uniqueness of the solution to a nonlinear parabolic equation
Journal Title: JOURNAL OF ADVANCES IN MATHEMATICS - Year 2018, Vol 14, Issue 2
Abstract
Consider the equation u’ (t) - u + | u |p u = 0, u(0) = u0(x), (1), where u’ := du/dt , p = const > 0, x E R3, t > 0. Assume that u0 is a smooth and decaying function, ||u0|| = sup |u(x, t)|. x E R3 ,t E R+ It is proved that problem (1) has a unique global solution and this solution satisfies the following estimate ||u(x, t)|| < c, where c > 0 does not depend on x, t.
Authors and Affiliations
Alexander G. Ramm
Keywords
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- EP ID EP651871
- DOI 10.24297/jam.v14i2.7503
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