Stability of global solutions to one-phase Stefan problem for a semilinear parabolic equation
Motion of spirals by crystalline curvature
Reorthoganization in the block Lanczos algorithm
Motion of spirals by crystalline curvature
Modern physics theories claim that the dynamics of interfaces between the two-phase is described by the evolution equations involving the curvature and various kinematic energies. We consider the motion of spiral-shaped polygonal curves by its crystalline curvature, which deserves a mathematical model of real crystals. Exploiting the comparison principle, we show the local existence and uniqueness of the solution.
Computational technique for treating the nonlinear Black-Scholes equation with the effect of transaction costs
We deal with numerical computation of the nonlinear partial differential equations (PDEs) of Black–Scholes type which incorporate the effect of transaction costs. Our proposed technique surmounts the difficulty of infinite domains and unbounded values of the solutions. Numerical implementation shows the validity of our scheme.
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