in this paper, heir-equations method is applied to investigate nonclassical symmetries and new solutions of the black-scholes equation. nonlinear self-adjointness is proved and infinite number of conservation laws are computed by a new conservation laws theorem.

In this paper, Heir-equations method is applied to investigate nonclassical symmetries and new solutions of the Black-Scholes equation. Nonlinear self-adjointness is proved and infinite number of conservation laws are computed by a new conservation laws theorem.

We analyze the discretization of nonlinear parabolic equations in Hilbert spaces by both implicit and implicit–explicit multistep methods and establish local stability under best possible and best possible linear stability conditions, respectively. Our approach is based on suitable quantifications of the non-self-adjointness of linear elliptic operators and a discrete perturbation argument.

The paper is devoted to the Lie group analysis of a nonlinear equation arising in metallurgical applications Magnetohydrodynamics. Self-adjointness basic equations investigated. reveals two exceptional values exponent playing significant role model.

We develop the concept of operators in Hilbert spaces which are similar to their adjoints via antiunitary operators, latter being not necessarily involutive. discuss extension theory, refined polar and singular-value decompositions, antilinear eigenfunction expansions. The study is motivated by physical symmetries quantum mechanics with non-self-adjoint operators.

The symmetry group method is applied to study a class of time-fractional generalized porous media equations with Riemann–Liouville fractional derivatives. All point groups and the corresponding optimal subgroups are determined. Then, similarity reduction performed given equation some explicit solutions derived. asymptotic behaviours for also discussed. Through concept nonlinear self-adjointness...