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Continuous dependence of 2D large scale primitive equations on the boundary conditions in oceanic dynamics

Yuanfei Li, Shengzhong Xiao (2022)

Applications of Mathematics

In this paper, we consider an initial boundary value problem for the two-dimensional primitive equations of large scale oceanic dynamics. Assuming that the depth of the ocean is a positive constant, we establish rigorous a priori bounds of the solution to problem. With the aid of these a priori bounds, the continuous dependence of the solution on changes in the boundary terms is obtained.

Continuous dependence of the entropy solution of general parabolic equation

Mohamed Maliki (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

We consider the general parabolic equation : u t - Δ b ( u ) + d i v F ( u ) = f in Q = ] 0 , T [ × N , T > 0 with u 0 L ( N ) , for a ....

Continuous dependence on function parameters for superlinear Dirichlet problems

Aleksandra Orpel (2005)

Colloquium Mathematicae

We discuss the existence of solutions for a certain generalization of the membrane equation and their continuous dependence on function parameters. We apply variational methods and consider the PDE as the Euler-Lagrange equation for a certain integral functional, which is not necessarily convex and coercive. As a consequence of the duality theory we obtain variational principles for our problem and some numerical results concerning approximation of solutions.

Continuum spectrum for the linearized extremal eigenvalue problem with boundary reactions

Futoshi Takahashi (2014)

Mathematica Bohemica

We study the semilinear problem with the boundary reaction - Δ u + u = 0 in Ω , u ν = λ f ( u ) on Ω , where Ω N , N 2 , is a smooth bounded domain, f : [ 0 , ) ( 0 , ) is a smooth, strictly positive, convex, increasing function which is superlinear at , and λ > 0 is a parameter. It is known that there exists an extremal parameter λ * > 0 such that a classical minimal solution exists for λ < λ * , and there is no solution for λ > λ * . Moreover, there is a unique weak solution u * corresponding to the parameter λ = λ * . In this paper, we continue to study the spectral properties of u * and show...

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