|Conţinutul numărului revistei|
| SM ISO690:2012|
CHOBAN, Mitrofan, MOROŞANU, Costică. Well-posedness of a nonlinear second-order anisotropic reaction-diffusion problem with nonlinear and inhomogeneous dynamic boundary conditions. In: Carpathian Journal of Mathematics, 2022, vol. 38, pp. 95-116. ISSN 1584-2851. DOI: 10.37193/CJM.2022.01.08
|Carpathian Journal of Mathematics|
|Volumul 38, / 2022 / ISSN 1584-2851 /ISSNe 1843-4401|
The paper is concerned with a qualitative analysis for a nonlinear second-order boundary value problem, endowed with nonlinear and inhomogeneous dynamic boundary conditions, extending the types of bounday conditions already studied. Under certain assumptions on the input data: f1 (t, x), w(t, x) and u0(x), we prove the well-posedness (the existence, a priori estimates, regularity and uniqueness) of a classical solution in the Sobolev space Wp1,2(Q). This extends previous works concerned with nonlinear dynamic boundary conditions, allowing to the present mathematical model to better approximate the real physical phenomena (the anisotropy effects, phase change in Ω and at the boundary ∂Ω, etc.).
Leray-Schauder principle, Nonlinear inhomogeneous dynamic boundary conditions, Nonlinear second-order anisotropic reaction-diffusion prblem, Qualitative properties of solutions