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EN
In this work we study ODE limit problems for reaction-diffusion equations for large diffusion and we study the sensitivity of nonlinear ODEs with respect to initial conditions and exponent parameters. Moreover, we prove continuity of the flow and weak upper semicontinuity of a family of global attractors for reaction-diffusion equations with spatially variable exponents when the exponents go to 2 in [formula] and the diffusion coefficients go to infinity.
EN
The uniqueness of classical solutions to inverse parabolic semilinear problems together with nonlocal initial conditions with integrals, for the operator [mathematical formula], in the cylindrical domain D:=D0×(t0,t0+T)[subset of]Rn+1, where t0[element of]R, 0
PL
W artykule studiowana jest jednoznaczność klasycznych rozwiązań odwrotnych parabolicznych semiliniowych zagadnień z nielokalnymi początkowymi warunkami z całkami dla operatora [wzór matematyczny], w walcowym obszarze D:=D0×(t0,t0+T)[podzbiór]Rn+1, gdzie t0[należy do]R, 0
EN
The uniqueness of classical solutions to parabolic semilinear problems together with nonlocal initial conditions with integrals, for the operator [mathematical equation] in the cylindrical domain D:= D0x(t0, t0 + T) ⊂ ℜn+1, where t0 ∈ ℜ, 0 < T < ∞, are studied. The result requires that the nonlocal conditions with integrals be introduced.
PL
W artykule omówiono jednoznaczność klasycznych rozwiązań parabolicznych semiliniowych zagadnień z nielokalnymi początkowymi warunkami z całkami dla operatora [równanie matematyczne], w walcowym obszarze D:= D0x(t0, t0 + T) ⊂ ℜn+1, gdzie t0 ∈ ℜ, 0 < T < ∞. Wynik polega na tym, że zostały wprowadzone warunki nielokalne z całkami.
4
Content available remote Strong maximum principles for infinite implicit systems with nonlocal inequalities
EN
The aim of the paper is to give strong maximum principles for infinite implicit systems of parabolic differential-functional inequalities with nonlocal inequalities together with sums in relatively arbitrary (n +1) − dimensional time - space sets more general than the cylindrical domain.
5
EN
The finite element method is applied in the time domain to establish formulations for the integration of second-order and hyperbolic (dynamic) problems. Modal decomposition in the space domain is used to recover the well-established method for uncoupling the equations of motion, which is extended to include general time approximation bases. The limitations of this approach in the implementation of large-scale, non-linear problems while preserving the uncoupling of the equations of motion are overcome by using the alternative concept of modal decomposition in the time domain. Both single- and double-field formulations are presented and the associated Trefftz formulations are established.
6
Content available remote Uniqueness of solutions to inverse parabolic problems
EN
The uniqueness of classical solutions to inverse parabolic semilinear problems together with nonstandard initial conditions, for the operator [formula].
7
Content available remote Theorems on impulsive parabolic differential-functional inequalities
EN
Theorems on weak parabolic differential-functional inequalities together with initial boundary inequalities and impulsive inequalities, and on uniqueness criteria of solutions of parabolic differential-functional problems in arbitrary parabolic sets are proved.
8
EN
In this paper we study impulsive nonlinear parabolic problems. For this purpose we prove three theorems on an estimate of absolute values of solutions of a mixed problem for impulsive parabolic equations, on estimates of the difference between two solutions of impulsive parabolic problems and on the uniqueness criterion of a solution of the first mixed impulsive parabolic problem. We apply properties of the theory of impulsive parabolic and ordinary problems.
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