Method of Rothe in evolution equations
On a degenerate parabolic boundary value problem
Numerical modeling of heat exchange and unsaturated-saturated flow in porous media
We discuss the numerical modeling of heat exchange between the infiltrated water and porous media matrix. An unsaturated-saturated flow is considered with boundary conditions reflecting the external driven forces. The developed numerical method is efficient and can be used for solving the inverse problems concerning determination of transmission coefficients for heat energy exchange inside and also on the boundary of porous media. Numerical experiments support our method.
On a Solution of Degenerate Elliptic-parabolic Systems in Orlicz-Sobolev Spaces II.
On a Solution of Degenerate Elliptic-parabolic Systems in Orlicz-Sobolev Spaces I.
Smoothing effect and regularity for linear parabolic equations
Stabilization of solutions of abstract parabolic equations
A generalized maximum principle and estimates of max vrai for nonlinear parabolic boundary value problems
On the solution of a generalized system of von Kármán equations
A nonlinear system of equations generalizing von Kármán equations is studied. The existence of a solution is proved and the relation between the solutions of the considered system and the solutions of von Kármán system is studied. The system considered is derived in a former paper by Lepig under the assumption of a nonlinear relation between the intensity of stresses and deformations in the constitutive law.
On boundedness of the weak solution for some class of quasilinear partial differential equations
On -convergence of Rothe’s method
On existence of the weak solution for non-linear partial differential equations of elliptic type. II.
On existence of the weak solution for non-linear partial differential equations of elliptic type
Method of Rothe and nonlinear parabolic boundary value problems of arbitrary order
Application of Rothe's method to perturbed linear hyperbolic equations and variational inequalities
Application of Rothe's method to nonlinear evolution equations
Nonlinear parabolic equations with the mixed nonlinear and nonstationary boundary conditions
Solution of porous medium type systems by linear approximation schemes.
On an approximate solution for quasilinear parabolic equations
Convergence of Rothe's method in Hölder spaces
The convergence of Rothe’s method in Hölder spaces is discussed. The obtained results are based on uniform boundedness of Rothe’s approximate solutions in Hölder spaces recently achieved by the first author. The convergence and its rate are derived inside a parabolic cylinder assuming an additional compatibility conditions.
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