Well-posedness of a nonlinear second-order anisotropic reaction-diffusion problem with nonlinear and inhomogeneous dynamic boundary conditions
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A Priori
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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: $f_{_1}(t,x)$, $w(t,x)$ and $u_0(x)$, we prove the well-posedness (the existence, a priori estimates, regularity and uniqueness) of a classical solution in the Sobolev space $W^{1,2}_p(Q)$. 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 $\Omega$ and at the boundary $\partial\Omega$, etc.).
2015 ◽
Vol 18
(2)
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pp. 225-250
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2020 ◽
Vol 25
(8)
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pp. 3135-3152
2004 ◽
Vol 200
(1)
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pp. 105-136
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2015 ◽
Vol 73
(1)
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pp. 93-129
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2004 ◽
Vol 356
(12)
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pp. 4787-4809
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