TAILIEUCHUNG - Explicit estimates on a mixed Neumann-Robin-Cauchy problem

The parabolic equation is of divergence form with discontinuous coefficients. We consider a nonlinear condition on a part of the boundary such that the power laws (and the Robin boundary condition) appear as particular cases. | Turk J Math (2016) 40: 1356 – 1373 ¨ ITAK ˙ c TUB ⃝ Turkish Journal of Mathematics doi: Research Article Explicit estimates on a mixed Neumann–Robin–Cauchy problem Luisa CONSIGLIERI∗ R. Tom` as da Fonseca 26, Pateo Central 1600-256, Lisbon, Portugal Received: • Accepted/Published Online: • Final Version: Abstract: We deal with the existence of weak solutions for a mixed Neumann–Robin–Cauchy problem. The existence results are based on global-in-time estimates of approximating solutions, and the passage to the limit exploits compactness techniques. We investigate explicit estimates for solutions of the parabolic equations with nonhomogeneous boundary conditions and distributional right-hand sides. The parabolic equation is of divergence form with discontinuous coefficients. We consider a nonlinear condition on a part of the boundary such that the power laws (and the Robin boundary condition) appear as particular cases. Key words: Mixed Neumann–Robin–Cauchy problem, discontinuous coefficient, bounded solution 1. Introduction The existence of solutions to partial differential equations (PDEs) is not sufficient whenever the main objective is their application to other branches of science. In industrial applications, physical fields (such as temperature or potentials) verify PDEs in divergence form with a nondifferentiable leading coefficient. Thus, they do not correspond to the classical solutions. There is a growing demand for the existence of quantitative estimates with explicit constants due to the application of fixed-point arguments [14, 17, 26]. The knowledge of the values of the involved constants in the estimates is crucial. The study of the Dirichlet–Cauchy problem is vast in the literature; see [2, 6, 15, 19–21, 23, 28] to mention a few. It is known that Dirichlet boundary conditions roughly approximate the reality. As a consequence, the study of the Cauchy problem under .

• Toán học
• Mixed Neumann Robin Cauchy problem
• Discontinuous coefficient
• Bounded solution
• Robin boundary condition
• Parabolic equation
• Prabolic equation
• Bi spaces
• Quasilinear parabolic equation
• Long time behavior of solutions
• Faedo Galerkin approximation
• Semilinear parabolic equation
• Blow up
• Numerical blow up time
• Variable reaction
• Dirichlet boundary
• Four step implicit
• Almost optimal
• Nonlinear parabolic equation
• Elliptic projection operators
• Partial differential equation
• Finite element method
• Normal mode
• Tonkin Gulf
• Mathematical approach
• Ocean acoustic computation
• Quenching behavior
• Non linear source
• Nonlinear source
• Continuity of the quenching time
• Adaptive method on the quenching time
• Neumann conditions
• Exhibit a solution
• Bài viết nghiên cứu khoa học
• Global attractor
• Grushin operator
• Gronwall inequality
• Gamma equation
• Maximum principle
• Monotone finite difference scheme
• Non uniform grid
• Quasi linear parabolic equation
• Scientific computing
• Two side estimates
• parabolic Ginzburg Landau
• subjects of mathematics
• science reports
• studied mathematics
• natural sciences
• scientific research
• Quasilinear degenerate parabolic equation
• Weighted p Laplacian operator
• Weak solution
• Compactness method
• Monotonicity method
• Hall effect
• Quantum kinetic equation
• Parabolic quantum wells
• Electron phonon interaction
• Mathematical and physical
• Cauchy Dirichlet problem
• Nonsmooth domains
• Conical points
• The regularity
• Absorption coefficient
• Asymmetric semi parabolic quantum wells
• Electron phonon scattering
• Electromagnetic wave
• báo cáo hóa học
• công trình nghiên cứu về hóa học
• tài liệu về hóa học
• cách trình bày báo cáo
• báo cáo khoa học
• Optimal control problem
• Finite difference method
• Inverse problem
• Linear parabolic equations
• Speed of convergence
• Backward heat problem
• Modified quasi Boundary value method
• Polar coordinates
• Ill posed problem