An Osgood condition for a semilinear reaction–diffusion equation with time-dependent generator

Villa-Morales, José

doi:10.1016/j.ajmsc.2014.07.001

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Cited by 2 publications

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“…The cases where A = −(−∆) α 2 is the fractional power of the Laplacian, 0 < α < 2, have been used in models of anomalous growth of certain fractal interfaces [16]. The articles [3,15,18,20,27,32,33,34] are only a few examples for the study of global existence and blow up in finite time of positive solutions.…”

Section: Introductionmentioning

confidence: 99%

Blow up and globality of solutions for a nonautonomous semilinear heat equation with Dirichlet condition

Ceballos-Lira

Pérez

2019

rev.colomb.mat

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In this paper we prove the local existence of a nonnegative mild solution for a nonautonomous semilinear heat equation with Dirichlet condition, and give sucient conditions for the globality and for the blow up infinite time of the mild solution. Our approach for the global existence goes back to the Weissler's technique and for the nite time blow up we uses the intrinsic ultracontractivity property of the semigroup generated by the diffusion operator.

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Section: Introductionmentioning

confidence: 99%

Blow up and globality of solutions for a nonautonomous semilinear heat equation with Dirichlet condition

Ceballos-Lira

Pérez

2019

rev.colomb.mat

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The Existence of Radial Solutions to the Schrödinger System Containing a Nonlinear Operator

Wang

Zhang

Yang

2022

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In this paper, we investigate a class of nonlinear Schrödinger systems containing a nonlinear operator under Osgood-type conditions. By employing the iterative technique, the existence conditions for entire positive radial solutions of the above problem are given under the cases where components μ and ν are bounded, μ and ν are blow-up, and one of the components is bounded, while the other is blow-up. Finally, we present two examples to verify our results.

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An Osgood condition for a semilinear reaction–diffusion equation with time-dependent generator

Cited by 2 publications

References 5 publications

Blow up and globality of solutions for a nonautonomous semilinear heat equation with Dirichlet condition

Blow up and globality of solutions for a nonautonomous semilinear heat equation with Dirichlet condition

The Existence of Radial Solutions to the Schrödinger System Containing a Nonlinear Operator

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