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We consider an inhomogeneous quasilinear parabolic inequality involving a convection term, and posed in a complete noncompact Riemannian manifold. Under certain assumptions on the Ricci curvature of the manifold, we establish sufficient conditions for the nonexistence of weak solutions. Next, some special cases are discussed. Notice that no restriction on the sign of solutions is imposed.

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A Quasi-Linear Parabolic Inequality with Convection in Riemannian Manifolds

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  • 发表日期：

    2026年

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  • Mohamed Jleli,
  • Bessem Samet,
  • Calogero Vetro

摘要

We consider an inhomogeneous quasilinear parabolic inequality involving a convection term, and posed in a complete noncompact Riemannian manifold. Under certain assumptions on the Ricci curvature of the manifold, we establish sufficient conditions for the nonexistence of weak solutions. Next, some special cases are discussed. Notice that no restriction on the sign of solutions is imposed.