Nonhomogeneous initial-boundary value problems for linear parabolic systems

Initial - Boundary Value Problems for Parabolic Equations

Degenerate Parabolic Initial-Boundary Value Problems*

in Hilbert space and their realizations in function spaces as initial-boundary value problems for partial differential equations which may contain degenerate or singular coefficients. The Cauchy problem consists of solving (1.1) subject to the initial condition Jdu(0) = h. We are concerned with the case where the solution is given by an analytic semigroup; it is this sense in which the Canchy p...

INITIAL-BOUNDARY VALUE PROBLEMS FOR LINEAR PDEs: THE ANALYTICITY APPROACH

It is well-known that the main difficulties associated with the study of initial-boundary value problems for linear PDEs is given by the presence of unknown boundary values in any method of solution. To deal efficiently with this difficulty, we have recently proposed two alternative (but interrelated) methods in Fourier space: the Analitycity approach and the Elimination by Restriction approach...

Reproducing Kernel Methods for Solving Linear Initial-boundary-value Problems

In this paper, a reproducing kernel with polynomial form is used for finding analytical and approximate solutions of a second-order hyperbolic equation with linear initial-boundary conditions. The analytical solution is represented as a series in the reproducing kernel space, and the approximate solution is obtained as an n-term summation. Error estimates are proved to converge to zero in the s...

INITIAL-BOUNDARY VALUE PROBLEMS FOR LINEAR AND SOLITON PDEs

Evolution PDEs for dispersive waves are considered in both linear and nonlinear integrable cases, and initial-boundary value problems associated with them are formulated in spectral space. A method of solution is presented, which is based on the elimination of the unknown boundary values by proper restrictions of the functional space and of the spectral variable complex domain. Illustrative exa...