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Existence of solutions for anisotropic parabolic Ni-Serrin type equations originated from a capillary phenomena with nonstandard growth nonlinearity.
  • Rabil Ayazoglu(Mashiyev),
  • Ebubekir Akkoyunlu,
  • Zohreh Naghizadeh
Rabil Ayazoglu(Mashiyev)
Bayburt University

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Ebubekir Akkoyunlu
Bayburt University
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Zohreh Naghizadeh
University of Science and Technology of Mazandaran
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We consider an initial boundary value problem for a class of anisotropic parabolic Ni-Serrin type equations with nonstandard nonlinearity in a bounded smooth domain with homogeneous Dirichlet boundary condition. Because the nonlinear perturbation leads to difficulties (it does not have a definite sign) in obtaining a priori estimates in the energy method, we had to modify the Tartar method significantly. Under suitable assumptions, we obtain the global existence, decay, and extinction of solutions.