On the critical exponent “instantaneous blow-up” versus “local solubility” in the Cauchy problem for a model equation of Sobolev type
М. О. Корпусов, А. Н. Панин, Andrey Shishkov
Abstract
Abstract We consider the Cauchy problem for a model partial differential equation of order three with a non-linearity of the form . We prove that when the Cauchy problem in has no local-in-time weak solution for a large class of initial functions, while when there is a local weak solution.
Topics & Concepts
MathematicsSobolev spaceExponentMathematical analysisCauchy distributionCritical exponentType (biology)Cauchy problemInitial value problemPure mathematicsGeometryScalingLinguisticsPhilosophyEcologyBiologyAdvanced Mathematical Physics ProblemsDifferential Equations and Boundary ProblemsNonlinear Partial Differential Equations