Abstract
The aim of this paper is to show some applications of Sobolev inequalities in partial differential equations. With the aid of some well-known inequalities, we derive the existence of global solution for the quasilinear parabolic equations. When the blow-up occurs, we derive the lower bound of the blow-up solution.
Highlights
Sobolev inequalities, called Sobolev imbedding theorems, belong to the issues of focus of current research, and play an important role in reality
We note two inequalities which are widely used in partial differential equations
We introduce the quasilinear parabolic equation and give our main results
Summary
Called Sobolev imbedding theorems, belong to the issues of focus of current research, and play an important role in reality. Inequalities are often related to the dimension of space. We note two inequalities which are widely used in partial differential equations (see [6, 14, 15, 19]). Lemma 1.1 Assume that ⊂ RN is a bounded, sufficiently smooth, connected domain with boundary ∂ of bounded curvature and supposing v ∈ C01( ).
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