Existence and blow-up of solutions for finitely degenerate semilinear parabolic equations with singular potentials
Huiyang Xu
Abstract
<abstract><p>In this article, we investigate the initial-boundary value problem for a class of finitely degenerate semilinear parabolic equations with singular potential term. By applying the Galerkin method and Banach fixed theorem we establish the local existence and uniqueness of the weak solution. On the other hand, by constructing a family of potential wells, we prove the global existence, the decay estimate and the finite time blow-up of solutions with subcritical or critical initial energy.</p></abstract>
Topics & Concepts
UniquenessDegenerate energy levelsMathematicsMathematical analysisParabolic partial differential equationBoundary value problemGalerkin methodClass (philosophy)Weak solutionInitial value problemPure mathematicsPartial differential equationPhysicsNonlinear systemQuantum mechanicsArtificial intelligenceComputer scienceNonlinear Partial Differential EquationsAdvanced Mathematical Physics ProblemsStability and Controllability of Differential Equations