On a nonlinear integro-differential equation
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The paper illustrates the mutual influence of the effects of nonlinearity and nonlocality, namely, an exact solution of the Cauchy problem for a nonlinear integro-differential equation is found, which has the following property: a change in the sign of a bounded initial condition in finite time leads to an unbounded increase in the modulus of the corresponding solution. A general solution of the Cauchy problem for the equation under consideration is obtained, and a method for expanding the Laplace transform tables by two variables using partial solutions of this equation is demonstrated.
Pre-image, transform table, convolution, bessel functions of the first kind, modified bessel functions, complex plane
Короткий адрес: https://sciup.org/147250357
IDR: 147250357