In the present paper, we study Cauchy problem for weakly coupled system of generalized Tricomi equations with multiple propagation speeds. Our aim this paper is to prove a small data blow-up result and an upper estimate lifespan suitable compactly supported initial in subcritical critical cases Strauss type. The proof based on framework argument [17]. One our new contributions construct two fam...

This note shows the existence of a sharp bilinear estimate for the Bourgain-type space and gives its application to the optimal local well/illposedness of the Cauchy problem for the Benjamin equation.

We solve the Cauchy problem for the Korteweg–de Vries equation with initial conditions which are steplike Schwartz-type perturbations of finitegap potentials under the assumption that the respective spectral bands either coincide or are disjoint.

Logarithmic convexity type continuous dependence results for discrete harmonic functions defined as solutions of the standard C" piecewise-linear approximation to Laplace's equation are proved. Using this result, error estimates for a regularizaron method for approximating the Cauchy problem for Poisson's equation on a rectangle are obtained. Numerical results are presented.

In this paper, we introduce $rho$-altering $J$-type mappings in modular spaces. We prove some fixed point theorems for $rho$-altering and $rho$-altering $J$-type mappings in modular spaces. We also furnish illustrative examples to express relationship between these mappings. As a consequence, the results are applied to the existence of solution of an integral equation arising from an ODE ...

We solve the Cauchy problem for the Korteweg–de Vries equation with initial conditions which are steplike Schwartz-type perturbations of finitegap potentials under the assumption that the mutual spectral bands either coincide or are disjoint.

This paper includes various parts of the theory of mixed type partial differential equations with initial and boundary conditions in fluid mechanics ,such as: The classical dynamical equation of mixed type due to Chaplygin (1904), regularity of solutions in the sense of Tricomi (1923) and in brief his fundamental idea leading to singular integral equations, and the new mixed type boundary value...