Existenzs�tze mit der linienmethode f�r parabolische probleme und periodische l�sungen von ut=f(t,x,u,ux,uxx)
Copyright policy )Existenzs�tze mit der linienmethode f�r parabolische probleme und periodische l�sungen von ut=f(t,x,u,ux,uxx)
The (longitudinal) method of lines transforms a parabolic equation into a first order system of ordinary differential equations by discretization of the spatial variable. It is shown how to obtain existence theorems for nonlinear parabolic equations from those for ordinary differential equations under general growth conditions and weak regularity assumptions. The method is demonstrated in proving a new existence theorem for periodic solutions to ut=f(t,x,u,ux,uxx) with boundary conditions of Dirichlet type.
- DigiZeitschriften Germany
- Karlsruhe Institute of Technology Germany
parabolic equation, a priori estimates, Numerical methods for partial differential equations, boundary value problems, method of lines, nonlinear parabolic equations, periodic solutions, Article, 510.mathematics, Initial-boundary value problems for second-order parabolic equations, ordinary differential equations, existence theorems, boundary conditions of Dirichlet type, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, dicretization of the spatial variable, Periodic solutions to PDEs, regularity assumptions
parabolic equation, a priori estimates, Numerical methods for partial differential equations, boundary value problems, method of lines, nonlinear parabolic equations, periodic solutions, Article, 510.mathematics, Initial-boundary value problems for second-order parabolic equations, ordinary differential equations, existence theorems, boundary conditions of Dirichlet type, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, dicretization of the spatial variable, Periodic solutions to PDEs, regularity assumptions
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