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.
On the solution of inverse problems for generalized oxygen consumption
We present the solution of some inverse problems for one-dimensional free boundary problems of oxygen consumption type, with a semilinear convection-diffusion-reaction parabolic equation. Using a fixed domain transformation (Landau’s transformation) the direct problem is reduced to a system of ODEs. To minimize the objective functionals in the inverse problems, we approximate the data by a finite number of parameters with respect to which automatic differentiation is applied.
Analysis of approximate solutions of coupled dynamical thermoelasticity and related problems
The authors study problems of existence and uniqueness of solutions of various variational formulations of the coupled problem of dynamical thermoelasticity and of the convergence of approximate solutions of these problems. First, the semidiscrete approximate solutions is defined, which is obtained by time discretization of the original variational problem by Euler’s backward formula. Under certain smoothness assumptions on the date authors prove existence and uniqueness of the solution and establish...
Application of Rothe's method to parabolic variational inequalities
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