Discrete and Continuous Dynamical Systems · 2009 · 22 citations · 7 references
Natural SciencesMathematicsPhysicsDifferential EquationsDynamical SystemsFluid DynamicsExistence TheoryNonlinear DynamicsPartial Differential EquationsPerturbation MethodsSingular Perturbation TheorySingularity AnalysisCauchy ProblemGlobal Existence TheoryNonlinearityParabolic Partial Differential EquationsSingular Perturbations In Partial Differential EquationsSingularitiesUniqueness In Nonlinear Differential Equations
We study the Cauchy problem for a parabolic partial differentialequation with a power nonlinearity.It was shown in our previous paper that in some parameter range, the problemhas a time-local solution with prescribed moving singularities.Our concern in this paper is the existence of a time-global solution.By using a perturbed Haraux-Weissler equation, it is shown that there existsa forward self-similar solution with a moving singularity.Using this result, we also obtain a sufficient conditionfor the global existence of solutions with a moving singularity.
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